One problem related to transfer case has been reported for the 2007 Chevrolet Avalanche. The most recently reported issues are listed below.
Complete transmission failure at 27,000 miles. Old part referenced as sun gear or sprag gear breakage between 4-wheel driver transfer case and transmission. Part failed under acceleration nearly causing a crash. Transmission would not engage gears except park. Vehicle could not move under its own power. Part is under back order and will take an unknown amount of time to fix. Other owners are experiencing the same problem around the same mileage. Gm was unresponsive to this common problem.