446. In The House: The prohibition against eating sin or guilt offerings outside the Temple
… your cattle and your flocks… (Deuteronomy 12:17)
While sacrifices of a lesser degree of sanctity might be eaten throughout Jerusalem, the korban chatas (sin offering) and the korban asham (guilt offering) had to be eaten within the Temple. This is true of anyone who might eat them, even the kohanim.
The reason for this mitzvah is that sacrifices had distinct reasons for being offered and they had locations to be eaten that were appropriate for their individual purposes. For example, as we have said regarding the korban chatas, "the kohanim eat it and the person bringing it is forgiven" (Talmud Pesachim 59b - see Mitzvah #102). Eating it in its proper place is an inherent part of the sacrifice. For the kohanim to deviate and eat of it elsewhere distracts their minds from the proper service and detracts from the sacrifice.
This mitzvah only applies at a time when the Temple service is in effect. It is discussed in the Talmud in tractate Makkos (17a-b). It is codified in the Mishneh Torah in the seventh chapter of Hilchos Maaseh HaKorbanos. This mitzvah is #145 of the 365 negative mitzvos in the Rambam’s Sefer HaMitzvos.