QUESTION: The Gemara (32b) discusses three cases which are the subject of a dispute between Rebbi Chiya and Bar Kapara. The first case is that of a non-Kohen (Zar) who performs an Avodah in the Beis ha'Mikdash on Shabbos ("Zar she'Shimesh b'Shabbos"). Rebbi Chiya maintains that he is Chayav for two transgressions -- for desecrating Shabbos, and for performing Avodah as a non-Kohen. Bar Kapara maintains that he is Chayav for only one transgression -- for performing Avodah as a non-Kohen.
The Gemara here explores the details of the case and the underlying point of dispute between Rebbi Chiya and Bar Kapara. Exactly what Avodah did the Zar perform? The Avodah cannot be the act of Shechitah of a Korban, because the Zar would not be Chayav for two transgressions for performing the Shechitah of a Korban on Shabbos; a Zar is permitted to perform the Shechitah of a Korban.
RASHI (33b, DH Shechitah b'Zar) comments that since a Zar may perform Shechitah, "there is no Isur of Zarus (performing an Avodah as a non-Kohen)." Rashi implies that a Zar who slaughters a public Korban on Shabbos will be liable for only one transgression (Chilul Shabbos).
Why is the Zar liable for Chilul Shabbos when he slaughters a Korban on Shabbos? If a Zar is permitted to perform the Shechitah of a Korban, his act should not constitute Chilul Shabbos when he performs the Shechitah of a public Korban on Shabbos! (SHA'AR HA'MELECH, Hilchos Bi'as Mikdash 6:10)
Moreover, the Mishnah in Pesachim (64a) states, "The same way it (the Korban Pesach) is offered during the week, it is offered on Shabbos." The Mishnah clearly says that the owner of the Korban Pesach, a Zar, may slaughter his Korban during the week. Accordingly, a Zar should be permitted to slaughter his Korban Pesach on Shabbos as well. (RASHASH)
ANSWER: Although a Zar's Shechitah is certainly valid, the Torah requires that l'Chatchilah a Kohen perform the Shechitah of any public Korban (such as the Korban Tamid), as the RITVA (Yoma 25a, DH u'Shtei Defanos) and ME'IRI (Yoma 25a, 31b) write. Since the Korban is offered on behalf of the Tzibur, it is appropriate that the Kohen -- who is the Tzibur's appointed Shali'ach -- perform the Shechitah of the Korban on their behalf. Since the Zar may not perform the Shechitah l'Chatchilah, if he does it on Shabbos he transgresses the Isur of slaughtering an animal on Shabbos. The Torah permits Shechitah on Shabbos only when it is done in a manner that is fully sanctioned l'Chatchilah. (As Rebbi Chiya says, "The Torah permits Avodah on Shabbos only for [those who are told to do the Avodah -- ] the Kohanim, not for Zarim.")
The Shechitah of the Korban Pesach is different. The Korban Pesach is privately owned, and for any privately-owned Korban there is a Mitzvah l'Chatchilah for the owner himself to slaughter the Korban (Rashi to Pesachim 7b, DH Pesach; see, however, Rashi to Pesachim 64a, DH Shachat Yisrael, and Insights to Pesachim 64:3). Therefore, a Zar is permitted to slaughter the Korban Pesach on Shabbos.
This answer is based on the premise that in any situation in which the Torah suspends a prohibition and permits a certain act to be done, it does not permit that act to be done when it is prohibited l'Chatchilah for some other reason. The CHIDUSHEI RABEINU MEIR SIMCHAH cites proof for this principle from the Gemara's explanation (33a) of the second case in which Rebbi Chiya and Bar Kapara disagree. When a Ba'al Mum (a Kohen with a blemish) performs an Avodah while he is Tamei, is he liable for two transgressions (performing an Avodah as a Ba'al Mum, and performing an Avodah while Tamei), or for only one transgression (performing an Avodah as a Ba'al Mum)? The Gemara explains that the case in question is when the two Isurim took effect at the same moment. Such a case exists when a Kohen became a Ba'al Mum by cutting off his finger with a knife that was Tamei. He became a Ba'al Mum at the same moment that he became Tamei. The RAMBAM (Hilchos Bi'as ha'Mikdash 8:11) counts a missing finger as one of the blemishes which invalidate a Kohen from performing an Avodah l'Chatchilah, but b'Di'eved his Avodah is valid. Although, normally, "Tum'ah Hutrah b'Tzibur" (the Kohen may perform the Avodah of a Korban Tzibur while he is Tamei, even l'Chatchilah), in this case the Kohen is liable for performing the Avodah while Tamei (according to Rebbi Chiya). Why should the Kohen be liable for performing the Avodah while Tamei, if "Tum'ah Hutrah b'Tzibur"? It is evident that "Tum'ah Hutrah b'Tzibur" does not apply when the Avodah is performed in a way in which, l'Chatchilah, it should not be performed -- such as by a Kohen who is missing a finger. (See also the Gemara earlier, 20b, with regard to Tefisas Yibum b'Di'eved with Chayavei Lavin.)