We are in Maseches Avos, chapter 4, mishnah 5 (in some editions of the Mishnah it is included at the end of mishnah 4). The speaker in our mishnah is Rabbi Yochanan ben Beroka. We do not know a great deal about him, but he appears in many mishnayos; he was a colleague of Rabbi Elazar Chisma, and both were students of Rabbi Yochanan ben Chananya.
The mishnah is extremely brief: "Kol hamechalel Shem Shamayim baseser - nifra'in mimenu bagalui, echad shogeg v'echad meizid b'chilul Hashem" - anyone who desecrates the Name of Heaven in private will be punished in public; and in the sin of chilul Hashem there is no difference between one who does so unintentionally, by mistake, and one who does so deliberately, with premeditation.
Two unique novelties in the prohibition of chilul Hashem:
Usually reward and punishment operate measure for measure; here we are told that even if the person acted in private, the payment is exacted publicly.
Usually we distinguish between unintentional and deliberate: one who desecrates Shabbos on purpose is nothing like one who did so by mistake. But in chilul Hashem this distinction does not exist.
We therefore need to clarify what chilul Hashem is and why it is judged so severely.
Explaining the words "chilul Hashem":
The word "Hashem" here does not refer to the ineffable four letter Name, the way we customarily call the Almighty "Hashem." Here it means the way in which human beings relate to the Almighty - and that is what a name is. The Almighty in Himself is what He is and does not change, whether or not anyone thinks about Him; but the way people relate to Him - that is what is called His Name. Just as a person is called by different names depending on the relationship someone has with him - an uncle to one person, a brother to another, a son or a friend - so too the Almighty can be related to in different ways. "Hashem," then, is the way the Almighty is related to here below.
The mitzvah of kiddush Hashem and the prohibition of chilul Hashem are two sides of one coin. They are two separate mitzvos out of the 613, and they are derived from the very same verse: on the one hand the Almighty says "v'nikdashti b'soch Bnei Yisrael," and from that very same source we also learn the prohibition against desecrating the Name of the Almighty. Let us explain both concepts, since each one teaches about the other:
Kedushah: a connection to what is beyond and above. That is why we make the berachah "asher kideshanu b'mitzvosav" - through the mitzvos we have a connection to what is above. When something is sanctified, it means that it is connected to what is beyond.
Chilul: the removal of that connection. This is also the technical halachic term: coins of maaser sheni that have sanctity invested in them, and one wishes to remove it from them - that is called chilul, the removal of the sanctity.
The root of the matter lies in the word "chalal" - ches, lamed, lamed. As a noun it means empty, as in the empty space of the world, something that has been emptied out. A son of a kohen born from a forbidden union is also called a "chalal" - he has been emptied of his priestly status. "Chilul Hashem," then, means that a person empties the presence of Hashem out of the world. Kiddush is to take this world and connect it to Hashem, and chilul is to empty out that connection and sever it.
Kiddush Hashem - the mission statement of the Jewish people:
The purpose for which our nation exists is kiddush Hashem, and everything else is a detail. As a private individual, a person is meant to be certain things - these are the six constant mitzvos: to live with love of Hashem, with fear of Him, and so on; and in terms of what he is meant to do, he has 613 individual mitzvos. But as the Jewish people collectively, we have one specific mission: kiddush Hashem.
This is why the Rambam brings the mitzvah of Kiddush Hashem right at the very beginning - in Hilchos Yesodei HaTorah, at the head of the fifth chapter. After establishing who Hashem is, how He relates to the world through the angels and the physical universe, and how we are to relate to Him, the first thing he writes is that "kol Beis Yisrael" - all of Klal Yisrael together - are commanded regarding Kiddush Hashem and warned against Chillul Hashem. This is what we are here for.
One who makes a Kiddush Hashem is therefore fulfilling the ultimate purpose of Klal Yisrael. And conversely, one who desecrates Hashem's Name - who causes people to take Hashem less seriously, to relate to Him as though He is not really here and does not really matter, Rachmana litzlan - that is Chillul Hashem, and it is the most severe of all. The Yerushalmi states explicitly (Niddah 3:9) that Chillul Hashem is the gravest sin there is, and so writes Rabbeinu Hillel in Shevuos chapter 12, that Chillul Hashem is the most severe of the transgressions; and from the positive you learn the negative - that its opposite side, Kiddush Hashem, is the most important of the mitzvos.
How many mitzvos are there for which a person is required to give up his life?
People commonly think the answer is three, but that is not so. There is only one - the mitzvah of Kiddush Hashem; or if you wish, two - the mitzvah of Kiddush Hashem and the prohibition of Chillul Hashem. All the parameters of when a person must give up his life and when he need not are all laws of Kiddush Hashem and Chillul Hashem, and they have no essential connection to murder, illicit relations or idolatry; those are merely details. This is not the place to enter into it, but there are times when a person must give up his life in certain situations even over a light matter, because this is not a rule about the transgression itself but a rule about Kiddush Hashem and Chillul Hashem.
This teaches us a great principle: the entire framework of the Torah is designed so that a person should fulfill "vachai bahem" - that he should live and attain the eternal connection with Hashem. That is what we are here to do: to develop a relationship with Hashem and to forge it, so that it will be our portion in the World to Come forever. And even so, there is something more important than that - Kiddush Hashem and Chillul Hashem - and therefore a person is sometimes required to give up his life rather than transgress certain things.
What is an act of Chillul Hashem?
Having defined the terms "chillul" and "Hashem," we need to define the act itself: causing Hashem to be perceived as less serious, less present, active and relevant in the world - whether in someone else's awareness or in a person's own awareness. And from here a question arises on our Mishnah: the Mishnah is dealing with someone who desecrates Hashem's Name in private, in secret, when nobody sees him. How, then, does he affect the awareness of others, when there is nobody there to see him?
The answer to this question is extremely important, because many people misunderstand the essence of Kiddush Hashem and Chillul Hashem. Some think that a Kiddush Hashem happens only when people look at a Jew and say, "See how pleasant the deeds of the Jews are," and sometimes they narrow it to non-Jews looking at Jews. But this is not the case at all: Chillul Hashem and Kiddush Hashem have no necessary connection to who is watching. So rules the Rambam in Hilchos Yesodei HaTorah chapter 5, halachah 10:
"Kol ha'over mida'ato... b'sha'at b'nefesh l'hach'is" - one who transgresses any of the mitzvos stated in the Torah willingly, without anyone forcing him, and out of contempt - he is desecrating Hashem's Name. Why? Because it happens even inside his own head: the way he relates to Hashem is weakened, and that alone is enough. He says to himself, "Look, I commit sins and Hashem does nothing, no lightning strikes me, nothing happens - apparently it does not interest Him," or perhaps even, "maybe Hashem is not real," chas v'shalom. That is a Chillul Hashem within his own awareness.
"V'chein kol haporesh mei'aveirah o asah mitzvah... lo mipnei davar ba'olam - lo pachad v'lo yirah v'lo l'vakesh kavod - ela mipnei haBorei" - one who refrains from a sin or performs a positive mitzvah not because of any external factor: not because he wants to avoid punishment, not because he does not want to look bad, and not because he wants people to think he is a good person. The only thing motivating him - and the Rambam is not speaking here of love or fear - is that Hashem exists, and Hashem said "do this" or "do not do this," and since Hashem said so, that is what I will do. Such a person sanctifies Hashem's Name.
The idea is that even within his own mind a person takes Hashem seriously: Hashem said - and I do. This strengthens Hashem's presence and sanctifies His Name, and causes this world to be more connected to awareness of Hashem, even when it takes place only inside a person's head. And this is a Kiddush Hashem even though nobody is watching - and this is the point of our Mishnah.
Therefore the Mishnah says that Kiddush Hashem and Chillul Hashem are so severe that they are treated differently from all other transgressions. As for the negative side, the desecration: even if a person acted in complete privacy and nobody saw, Hashem will exact payment from him, and quite possibly in public, so that the matter should come to light and everyone should know what he did. The details depend on how Hashem makes His calculations according to many factors, but the point is that although ordinarily a person would be granted leniency - that is not so with Chillul Hashem. Similarly, it makes no difference whether he intended to desecrate Hashem's Name or not: if the result is the result - the consequence is the consequence, unlike other matters.
The four categories of atonement:
At the end of the first chapter of Hilchos Teshuvah, the Rambam lists the four categories of atonement - four levels of sin and the way each one is atoned for - and the last level, the most severe of them all, is chillul Hashem. He writes that one who commits a serious sin of the gravest kinds, those carrying the death penalty or kareis, must do teshuvah, and the teshuvah suspends the punishment until Yom Kippur, and even after Yom Kippur suffering is still required. But he qualifies this: "When does this apply? When he did not desecrate the Name" - that is, when the act contained no element of chillul Hashem.
But one who did desecrate the Name - even though he did teshuvah, and Yom Kippur came, and he is standing firm in his teshuvah, and suffering has come upon him - even though he has done everything in his power, all three only suspend the matter. They stand and remain suspended, and he is left with the damage and the effect that the chillul Hashem caused, and it is not atoned for until death. For as long as he walks upon the earth, he himself is a living reminder of that act of chillul Hashem. Once he dies - provided, of course, that he has done all the earlier stages - he has no further punishment in the World to Come, but his complete atonement and purification are not achieved until the very end, since chillul Hashem is the gravest sin of them all.
In summary: In this Mishnah we learned two novel points about the sin of chillul Hashem: one who desecrates the Name in private is punished publicly, and there is no difference between an unintentional and an intentional act. We explained that "the Name" is the way the Holy One is related to here below, that sanctification is a connection to what is above and desecration is an emptying out of that connection; we saw that kiddush Hashem is the mission statement of the Jewish people as a collective, from which all the laws of self-sacrifice are derived; and we learned from the Rambam that chillul Hashem and kiddush Hashem take place even within a person's own consciousness, even when no one is watching.
And from here, as the Mishnah says, "echad shogeg ve'echad meizid" - it makes no difference whether it was done deliberately or by mistake, and therefore a person should be exceedingly careful not to come to chillul Hashem, Heaven forbid.