Originally Posted by Kayakado
It sounds like an adjustment but you can get a device called a dog tooth that will help prevent the chain falling off. It is a curved canine shaped piece of plastic that attaches to the down tube at about the height of the top of the inner chain ring and is a mechanical aid to keep that chain from coming too far off the teeth (it doesn't touch the chain)
Clarification- by "it doesn't touch the chain" don't you mean it doesn't touch during normal operation but touches the chain while performing its function of preventing the chain from overshooting during downshift?