Charles Ellicott Commentary Exodus 29:26

"And thou shalt take the breast of Aaron`s ram of consecration, and wave it for a wave-offering before Jehovah: and it shall be thy portion." — Exodus 29:26 (ASV)

You shall take the breast. —It was the general law that in “wave offerings” the breast was the officiating priest’s (Leviticus 7:29–31); therefore, on this occasion, it was assigned to Moses.