Generally speaking, no, they don't. In most cases, so long as you give them a dust bath once a week or so, they'll take care of grooming themselves.
I have heard about some people combing/brushing them when they're shedding, but I haven't found this to be necessary myself. I will sometimes help her remove some loose clumps of shedding fur with my fingers, but that's about it (and even that probably isn't necessary, but I kinda enjoy doing it and my chin doesn't seem to mind).
The only time that chins really require grooming is if their fur has become really tangled and matted. In those cases, you basically have to tug on the mats with a comb and/or your fingers until the matted fur pulls out (fur slips), which usually leaves a bald patch until the fur regrows. It's my understanding that matted fur is relatively uncommon among chins so long as they're given proper care (good diet, enrichment, dust baths given with proper frequency, etc.).
So I guess the answer to your question is that chins don't usually require any special grooming beyond weekly dust baths. With proper care, they're usually able to keep their coats in good condition on their own.
I've also never felt the need to trim my chin's nails. I do give her a lava ledge (basically a little ledge made out of pumice stone), which is supposed to help grind down their nails, but unless their nails have become rely overgrown for some reason, you generally don't need to trim them.
