The Right Thigh

The Sforno explains the significance of the thigh of the Peace offering that is given to the Kohen, as well as the additional gift of the arm from the Peace offering of the Nazir.

The thigh is connected to the foot while the arm is connected to the hand. Since the Kohen can enter holy places in the Mikdash that the Jew that offers the sacrifice cannot enter, thus, the Kohen is entitled to a part connected to the foot. The Nazir adds a part connected to the hand indicating that until this time the actions of the Nazir were restricted by his vow (given over to the holy) but now the hand of the former Nazir is once again in his domain and control.