What kind of hammock is it? Unless it's made completely of fleece, it should be removed (like the ones made for ferrets). Even then, you need to make sure the chin doesn't chew the fleece. Most don't, but there are a few that do.
The hammock probably has the nylon straps on it if it comes with a petstore cage. These are VERY VERY dangerous because a chinchilla can get its leg wrapped up in the straps and get injured. I have a chinchilla now that is missing a leg because her former owner used one of those hammocks (a month after I told her to take it down.)
It's important to remember that just because the packaging says that something is safe for chins it doesn't mean that it really is. Be careful with what you buy for your chinnies!
Unless they are made completely out of fleece, then no they aren't safe. I wouldn't push your luck with it just in case something did happen!
You can always make your own with a peice of fleece. I got a pretty big peice of scrape fleece at walmart for 5 dollars, enough to cover the cage pan and make a hammock made fully out of fleece with fleece straps!