Most of the chucks I've purchased over the years have come from used equipment dealers. Between the 2 lathes I have well over a dozen 3 and 4 jaw chucks ranging in size from 3" to 10". The only one purchased new was the 3" one. All the others were $100.00 or less from equipment dealers.
One lathe uses the L00 series mount while the other uses a 1 7/16- 12 threaded mount. I've either modified existing backplates or made new ones for the 1 7/16-12 spindle. If you can find a good used chuck you can get a partially finished backplate from a number of vendors on eBay.
I've bought chucks on eBay, from equipment dealers, and new.
New is obvious- pay a lot, get the best possible chuck, be happy. Or, pay less than you should, get a lump of Chinese recycling with tooling marks in it, and do it again until you're happy.
Equipment dealers mostly have equipment that was removed in serviceable condition from a working shop. This is where you buy a brand name for a decent price, but still probably pay more than you want to, but come away with a quality part that will last a lifetime. This is where I have had the most success getting excellent equipment used. Bang for the buck.
Used/classifieds/ebay- there are good deals for the patient, but it's always a gamble. There are chucks on ebay listed for tall stacks of cash that belong in the recycling bin. I've bought 4 chucks on ebay, and done good, but I am patient with my spending and exercise a high level of scrutiny, rejecting unrealistic prices and keying in on signs of wear, rejecting anything bellmouthed or obviously used beyond the sell-by date.