Don Teach commented that chucks for small size drills can be hard to
find.  McMaster Carr ( http://www.mcmaster.com/ ) has adapters for
drills in the 1/16" to 1/4" size (part no 3185A41 through 3185A54).
From the picture I believe these are the "Snappy" brand collet style
adapter I am using with great success.

I have also used a pin vise that had a chuck on only one end, or had
one end cut off so you have a smooth shank.  I could chuck it in my
regular drill press chuck.

John Dewey