Charles Ellicott Commentary Leviticus 8:29

"And Moses took the breast, and waved it for a wave-offering before Jehovah: it was Moses` portion of the ram of consecration; as Jehovah commanded Moses." — Leviticus 8:29 (ASV)

And Moses took the breast. —That is, the breast-piece, which afterward became the rightful portion of the officiating priest , fell in this instance to Moses' share, in accordance with the directions given in Exodus 29:26, to be his sacrificial meal, since he was divinely appointed to perform the priestly service.