Good fortune or chancellor
Chaunice is a modern American elaboration of the name Chauncey. It likely derives from the Old French word 'chance' meaning luck, or from the Latin 'cancellarius' referring to a high-ranking official or record keeper.
Less common today
Chaunice isn't in the latest US Top 1000. It last peaked at #8,593 in 1993.
US births per 5-year period, 1990βpresent (SSA data).