A cleaning of the spindle hole and the chuck arbor with some solvent and the "gentle" application of a wooden block should resolve your problem with about a 99% certainty.
You should also check the chuck arbor for tiny nicks or burrs that might impede a good fit. A light sanding with fine grit sandpaper (say 600 grit or finer) might help.
And as an obscure possibility, check the size of the taper on your drill chuck. Some drill chucks come with a Jacobs taper rather than with a Morse taper and they look very similar to the naked eye.
Where are all of the machinists out there?? What is the correct technical name of the hole in the end of the spindle that accepts the chuck arbor?? Most folks refer to it as the Morse taper; but I am pretty sure that is not correct. "Morse taper" describes the size and shape of the hole; but I think the hole, itself, has some other name.
Help!!!