Chaunce \cha(un)-ce\ as a boy's name is a variant of Chance (Middle English) and Chancellor (French, Middle English), and the meaning of Chaunce is "good fortune; office holder".
The baby name Chaunce sounds like Chauncy and Chauncey. Other similar baby names are Chanze, Chanse, Channe, Chayce, Chace, Chawncey, Chaunsy, Chaunsey, Chancey, Chayne, Chane and Launce.