How to keep rigidbody from falling through terrain?

Create the ground without a rigidbody, and place a collider on it instead. Your ground probably doesn't need to react to physics, but your object will need to react to physics so it will need a riggidbody on it AND a collider as well. You then place a Physics Material on the ground collider (which is optional) to apply either friction and/or bounciness to your player or game object.

Cool thanks. I have removed the rigidbody from the terrain. I think part of the problem was that I was placing a rigidbody along with the Character controller, and there were two forces at work. I have removed the rigidbody from the Player gameobject. It seems to be working fine now.