If the chain is falling off, the bike is shifting, just to a ring that doesn't exist. No chain rub isn't the issue and in fact is likely your problem. You want to tighten the outboard stop to if anything have a bit of chain rub on your derailleur when you shift up onto the big ring. It maybe a confluence of things as mentioned...slightly bent chainring...btw you can straight them...check the runnout...or a bad chain but it may simply be your stop. The chain will have a hard time shifting over the outboard ring if the stop is tight.