As far as I'm aware - the youngest Champion of a Challenger Tour event was Michael ChangMichael Chang when he won a Challenger event in Las Vegas in 1987 when he was 15 years and 7 months old. Not that surprising considering he also won the French Open at 17.
From what I remember hearing also - Richard GasquetRichard Gasquet was pretty young when he started winning Futures and Challengers as well - while he was 16 I think.
I'll try to find some sources to back up my claims and come back here and edit this answer afterwards.
Two sources found by Martin (in the comments)