Two things to help with your multi-speed chain problems. First is you need to get whats called a Jump Stop SBP has them Sick Bike Parts or you may be able to get one at your local bike shop.
If your chain falls inward, use the Jump-Stop. If your chain falls outward, install a front derailleur. If your chain falls inward AND outward, install the derailleur directly above the Jump-Stop.
