One problem related to driveshaft has been reported for the 2007 Chevrolet Silverado. The most recently reported issues are listed below.
Thump after coming to a stop. After about 24,000 miles. I started feeling a light thump from the rear, as if someone bumped me from behind. Over the next few weeks it became very noticeable, so I took it to the dealer for investigation. The 1st time, they said the rear-end had the wrong lube in it & they replaced it. This seem to work for the next several weeks. Then the thump returned lightly at 1st & gradually worsened to a major thump. I returned it to the dealer & this second repair was that the lubed the rear-end & replaced the yoke on the driveshaft. This repair worked for about a week & I started feeling the light thump again. I took it back in again, left it all day & they apparently drove it around the parking lot & couldn't duplicate the problem. One of the service managers rode with me, around the parking lot & the problem wouldn't show up. It has since worsened again & I will take it back in once the problem gets a little worse.