One of the biggest faults my students suffer from while chipping is over-active wrists. A chip shot should be considered a putt, but with a wedge. Despite having the ball slightly farther back in your stance, the swing motions are identical.
A chip should be performed with little to no wrist movement. Limiting your wrists will greatly reduce your chances of hitting your shot thin or heavy. I understand how this may be a difficult feeling to copy, especially considering most swings are performed with wrist action, but trust me, the work will be worth the results. To help incorporate this technique into your chipping game, try this drill.
Grab two clubs, flip one over and proceed to grip them normally (you will need to flip one of the clubs upside down to do this properly as seen in the picture above). The upside-down club will be coming up by your lead ear, as shown. For those of you more experienced in golf lingo you will need to have a forward press. Start without a ball, and simply work on your chipping stroke making sure your setup is sound. You will notice how the extra club will make using your wrists nearly impossible. Next try this drill hitting golf balls. With practice you will notice a definite improvement in your distance control, consistency and accuracy.