Yeah they shed, but I don't notice clumps of fur like with a cat or dog, even when I had around a dozen chins at one time. Chins don't shed all the time either, just a few times a year. Most of the fur seems to be in and around the cage and that gets vacuumed up during daily cleaning along with the poops. Also as I said before, during priming (shedding), all you really need to do is give a few extra dust baths to help the fur work it's way out. You do end up with some fur in the dust bath as well.
I'm not saying not to comb the chin if you want to, just that it's not required. A healthy well cared for chin's fur shouldn't need to be combed to prevent matting or anything. With regular dust baths the fur should naturally all shed out without issue and without the human needing to do anything. It will for sure cut down on the amount of fur around the cage if you do comb them during shedding though. The chin will also look better during the shedding if you comb the fur out too, some chins shed weird (in patches rather then in a nice line) and can look scruffy during shedding.
Maybe your chins shed more then my 2 guys, or you didn't vacuum everyday? When I clean the filter in my ac in the summer, I only have to do it about once or twice a month, and it's normally because of dust buildup not layers of fur.