The priests were allowed to have the thigh of the peace offering, but the breast was reserved for Aaron and his sons. This was a statute God instituted when he appointed them to serve the Lord. This is not a deeply theological principle, but it does demonstrate the fact that God is faithful to his word. What God promised well before the Levitical Code was begun held true throughout the Temple worship period of Israel. God is faithful!
This section ends with a summation of what laws God has established for the system of sacrificial worship.
Leviticus 7:37–38 (NKJV)
37 This is the law of the burnt offering, the grain offering, the sin offering, the trespass offering, the consecrations, and the sacrifice of the peace offering, 38 which the Lord commanded Moses on Mount Sinai, on the day when He commanded the children of Israel to offer their offerings to the Lord in the Wilderness of Sinai.