Two quick methods of determining - you have a worn chain if the chain can be lifted significantly off the front of the chainring while the rest of the drive train is at proper tension and meshed with the teeth (in other words everything is set up as if you'd be riding and you can just yank the chain away from the front of the chainring.
If the chain fails the lift-off test, then put a good quality ruler up to the chain and pick a rivet. Measure going along the length of the ruler to see if the rivets deviate from where they should be on the ruler. A very small amount is OK, but if we're talking 3/32"+ deviation then it's a worn chain. Running a worn chain is actually penny wise, pound foolish - it will accelerate wear on the more expensive chainring and cog parts.
If you're worried about the chain snapping - replace it, or at least carry a spare length of chain in the bag and a breaker tool.