Kiddushin 53 - Betrothal with a Priest's Portion of Sacrifices
If a priest betroths a woman with his portion of the sacrificial offering, whether most-holy (such as burnt-offering and sin-offering) or an offering of lesser holiness (such as peace offering and thanks-offering), she is not betrothed. The portions allotted to the priest and the owner of the offering are not theirs, but rather Divine property which they are merely permitted to eat.
But it may be asked, how can a woman come in the Inner Temple courtyard to accept Kiddushin? Her father can accept her Kiddushin, she can appoint an agent, or she can force her way in!