Diagnosis
The keyless chuck's internal jaws or the spindle lock mechanism are worn or contaminated with debris.
How to Fix It
Fully insert a bit. Grip the chuck sleeve firmly with one hand. Run the drill in reverse (left) at full trigger pull for 3-5 seconds. This often re-seats the jaws. Then, hand-tighten the chuck as hard as you can. Do not use pliers on the plastic sleeve.
If That Didn't Work
The chuck needs replacement. It's a standard ½-inch 20T keyless chuck. You need a 10mm Allen key to remove the retaining screw inside the jaws (it has left-hand threads). Unscrew clockwise to remove it, then the chuck unscrews counter-clockwise from the spindle.
Heads Up
The retaining screw is reverse-threaded. Turning it the wrong way will strip it. Use the correct size Allen key and significant force.