Your Chevy truck will tow it, but like others have said it will be marginal. I don't know where your dealer came up with that weight figure, I suspect he quoted the boat weight, forgot about the figure as not including engines or trailer.
My CD is on the lighter side of most others, it has less equipment. It weighed 7,500 lbs with my 27ft, galvanized steel, bunk type Pacific trailer with spare wheel and side bunks, full fuel tank, 1/2 water, dink, and overnight gear aboard. As Jim said, trailer is about 2,000 lbs or a bit more. An aluminum trailer would drop that weight by 500-700 lbs.
I tow mine with a 2003 Expedition 4x4 and 5.4L engine, same tow rating as your Chevy, 8,700 lbs (8,900 w/o 4x4). As Pat experienced, it is OK on flats but you have to be patient on hills of most any size, 2nd gear is the norm, steeper is 1st gear at 30-35 mph. I accept it because we use our Expedition as our family cruiser for trips on land, gets 18-20 non-towing. Plus I have a 22ft travel trailer to pull occasionally.
After you get your boat, it would be interesting to weigh it soon after with known fuel/water on board and list the equipment on board. Then a year or two later take it back to the same scale and weigh again, and also modify your list of equipment. It will probably surprise you. Congrats on your upcoming boat, it's a keeper!