I have the same B&D mains! What happens to these chucks is the end up with dust from drilling masonry! Never try to Grease the chuck. use and releasing fluid WD 40 or generic. Spray down inside the chuck. Place a spanner on the the nut at the the back of the chuck , it requires a standard open Jaw spanner I used a 3/4 Af. Take circular wrench and hold it on the outer side on the chuck and gently turn counter clockwise! Chuck to you right spanner on the base of the chuck and turn the out case of the chuck away from you gently! Then give it regular clean with releasing fluid!
Regards. Fred.