Sure, just buy a new chuck. Keep in mind, a crappy chuck is a crappy chuck
no matter if it is keyed or not. There are some good keyless chucks
available that probably cost more than the Skil brand drill.
Most chucks are held on by a bold with an allen head in the bottom. It is a
reverse thread. Take that out first. Sometimes you have to put the allen
wrench into (short end in) the chuck and rap it with a hammer to loosen it.
My recommendation too. The only keyless chuck drill I bought at a
garage sale had an integral shaft to the motor drive. The chuck is
not removeable from this shaft. My impression is drills are so cheap
nowadays (essentially throwaways) that they might as well save on the
manufacture and assembly of a gear train. Nobody repairs drills to
Once you loosen and remove the screw inside the chuck, you have to
remove the chuck from the shaft. To do that, you may have to put an
allen wrench in the chuck, tighten it down, and rap it with something
heavy. Sort of like was suggested for the screw in the chuck. Except
CCW iirc. (You can tell that by looking at the threads inside the
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