I have a 2011 Silverado LTZ 4x4 with Max Trailer tow package. Great truck, I purchased it new and it always used a bit of oil from the start - about 1 Qt per 3K miles. At about 30K, started using more oil - no leaks, no smoke. Burning / using about 2 quarts every 3K miles.
I brought truck to dealership where purchased, they did an oil consumption test (takes some time, and several visits to dealership) and found that motor was consuming more oil than normal. Chevy has agreed to address the problem - will report back on the fix once complete.
If you are having similar problems, be persistent and take truck to dealer - I am thinking that Chevy will want to to the right thing and correct the issue. They did for me.