Bicycle Chain Line
Bad chain line will cause the chain to come off the front rings when it shouldn't.
Bicycle chain line is the orientation of the chain to the centerline of the bike. Chain line is ideal when a line drawn from the center of the front gears to the center of the rear gears is parallel to the centerline of the bike.
The centerline of the bike is a line drawn from the center of the fork head tube to the center of the rear axle. Imagine a plane along this line centered on the bike: this would be the plane of the bike. On a properly aligned frame the plane of the bike will intersect the center of the front axle, the head tube, the seat tube, the down tube, the top tube, the bottom bracket shell, and the rear axle.
Test Chain Line
Put the bike in a work stand. Shift to the middle ring on a 3 gear crankset. Shift to the middle cog on the back, or one of the 2 most-middle cogs on an even-numbered cogset. Stand behind the bike and look along the chain line. Imagine the centerline of the bike. Does it look almost parallel to you?
Of course, that's a lousy way to judge chain line. There's a formula, but to use it you have to take measurements that are not practical to get precise enough for decent results. The best test is through experimentation and analysis.
An old bike does not suddenly develop a bad chain line. If the old steed starts throwing the chain, it's a different problem--probably a stretched chain and/or a worn or damaged cogset or chainring.
If you just bought a new bike, the chain line can be bad. If you just added new components, especially a new crankset, the new part can change the chain line. So, if your bike throws the chain off a chainring when it shouldn't, suspect chain line.
To test for bad chain line:
Put the bike in a work stand.
On a 3 speed crankset, shift to the middle ring. You should be able to shift to all rear gears without throwing the chain.
Shift to the big ring. Ideally you should be able to shift to all cogs without throwing the chain. However, you should never ride in the big ring and one of the larger cogs, because the "crossed chain" position stresses the chain too much. It's not a big deal not to be able to do what you shouldn't--ride with a crossed chain. Nevertheless, if the bike throws the chain, bad chain line is indicated.
Try the same thing in the small ring.
On a 2 speed crankset, test whether you can shift into all the cogs from each chainring. If you can't, bad chain line is indicated.
A chainring can be bent, or the teeth damaged, even on a new bike, so eliminate that possibility. While rotating the pedals, examine the suspect ring for a bend or damage.
Fix Bad Chain Line
The fix for a bad chain line is to install either a longer or shorter bottom bracket axle. This may be necessary even on a brand new bike, and is likely to be necessary anytime you upgrade from a cheap crankset to a nice one.