Chucks need to be kept clean but it's just as important to keep the spindle nose threads onto which the chuck threads clean and tidy.

My procedure, done before every mounting of a chuck, goes like this...

Put an oily toothbrush on the threads as far to the left (i.e. near the headstock) as possible and run the lathe in reverse at a low speed. The brush will be "unwound" along the threads and move to the right. As it does, it will sweep swarf before it and oil the threads to ease removal of the chuck in the future.

Easy to do, only takes a minute, and can save you from a lot of grief later on.