Just went through this last year, however you problem is total weight. The chevy is a little light in the tow cap compared to the Dodge, ford, and toyota.
However, my main concern is your total weight. Finding a trailer that is under 3,000 will be tough not to mention you have to leave room for chains, binders, etc.
Personally, I run a 011 Dodge ram with goosneck and airbags, but I am liscensed at 9990, and the trailer is 3750, and pulls a 5000lbs tractor.
So can it be done, of course, but you are asking for trouble. Also depends on what part of the country you are in, here in OH, KY, and PA, I won't dare push my luck.