Those are the simple ideas. Derailling of the chain from a single chainring used with a multi-speed rear is a frequently reported problem and the usual preventative is a fixed-in-place front derailleur or an outer chain guard and an inner chain watcher.

The problem may be exacerbated by your chainring. If it has the shaped teeth, ramps and other modern shifting enhancements it will make the situation worse. A "flat" old style or track, fixed gear or single speed chainring might reduce the spilling tendency.