Grease certainly attracts debris. If it is a scroll chuck (i.e. as in a common 3 jaw), then you ought to grease the ring gear and pinions. Use a heavy grease and don't load too much in. How to lube the face scroll & jaw mesh is a subject for debate (some chucks even have a lube fitting on the face of the chuck). I grease the face scroll, and it does attact chips. Occasionally I take my chucks apart and clean them (even if you don't grease the scroll, chips will still get in and a person ought to clean it out every once in a while).
If it is an independent jaw chuck (i.e. as in a common 4 jaw) - clean and oil the screws and slide fits (way lube). Then they won't load up with chips as much, and you can easily back the jaw right out and blow the chips out (good access for the air blowing the chips and the screws are a pain to remove, at least they are on my two 4 jaw chucks that get the most use).
Rohm recommends grease lubrication (see various locations on the internet).
"Lathe chucks must be lubricated regularly to maintain their
gripping force. Appropriate directions are included in the operating
instructions supplied with each chuck. All lathe chucks
are equipped with grease nipples for convenient maintenance."
It may well be that higher end, modern chucks are better protected from bringing chips in than the equipment that I have?