It’s peace: "hold your peace" equalling "maintain your silence".
The phrase occurs frequently in the Bible—suggesting it was very current at the time of that book’s first translation into English (it seems to correspond to the Hebrew root HSH, meaning "hush, keep silent, be still")—and its most famous liturgical use is in the wedding-ceremony formula: "Speak now, or forever hold your peace".
As to peace/piece, I am reminded of a teacher from my school days who would almost always—provoking that helplessly enraged "Oh, no: he’s going to say it again" feeling—dismiss classes who were leaving the room a little noisily with the words: "Depart in peace and not in pieces".
Coemgenus