Nazir chapter 7, mishnah 1. A Kohen Gadol and a nazir are both forbidden to become tamei even for their close relatives, and in this their law differs from that of an ordinary kohen, who is permitted to become tamei for his relatives but not for anyone else. And even though a Kohen Gadol and a nazir do not become tamei for their relatives, they are permitted to become tamei for a meis mitzvah - a corpse that has no one to attend to it and bury it.
The question the mishnah grapples with is: what is the law when there is a clash between a Kohen Gadol and a nazir - which of them is required to become tamei? And as we will see, there is even an opinion that the question does not concern only a Kohen Gadol, but an ordinary kohen as well.
The words of the mishnah:
"Kohen Gadol v'nazir eino mitamei bikroveihen" - as we mentioned, they do not become tamei even when a family member of theirs dies. But when they encounter a meis mitzvah, a corpse that has no one to attend to it and bury it, this law overrides his being a nazir or his being a Kohen Gadol.
"Hayu mehalchin baderech u'matz'u meis mitzvah" - the two of them were walking together on the road and found a meis mitzvah, with no one to attend to it besides them. In this law they disagreed:
Rabbi Eliezer: "Yitamei Kohen Gadol v'al yitamei nazir" - the Kohen Gadol is the one who should become tamei, and not the nazir.
And the Sages say the opposite: "Yitamei nazir v'al yitamei Kohen Gadol" - the nazir is the one who should become tamei. And in fact, as will become clear, this is said not only regarding a Kohen Gadol but even regarding an ordinary kohen: between an ordinary kohen and a nazir, it is the nazir who becomes tamei.
The reasoning of each side:
"Amar lahem Rabbi Eliezer: yitamei kohen she'eino meivi korban al tumaso, v'al yitamei nazir shehu meivi korban al tumaso" - it is better that the kohen become tamei, since he does not bring a korban after becoming tamei, rather than the nazir, since a nazir who became tamei is obligated to bring a korban for his tumah. From here we see that the tumah of a nazir is more severe, and therefore it is not set aside in favor of a kohen or a Kohen Gadol.
"Amru lo: lo, yitamei nazir she'ein kedushaso kedushas olam, v'al yitamei kohen shekedushaso kedushas olam" - the Sages answered him with the opposite argument: the nazir should become tamei, since his sanctity is not a sanctity that lasts forever and does not pass on to future generations; whereas the kohen - and the mishnah here says simply "kohen," to include even an ordinary kohen - should not become tamei when there is a choice between a kohen and a nazir, because his sanctity passes from generation to generation, unlike the sanctity of the nazir.
In summary: we learned that a Kohen Gadol and a nazir do not become tamei for their relatives, but they do become tamei for a meis mitzvah. When the two of them together encountered a meis mitzvah, there is a dispute as to which of them becomes tamei: Rabbi Eliezer holds that the Kohen Gadol becomes tamei, since he does not bring a korban for his tumah, while the Sages hold that the nazir becomes tamei, since his sanctity is not an eternal sanctity - unlike the sanctity of a kohen, even an ordinary kohen, which passes from generation to generation.