I’ve got a high-zoot road bike with sixteen speeds: an eight-cog cassette in back and two chainrings up front. Everything works just as it’s supposed to except once in a while the chain comes off the inner chainring.
Everything appears to be adjusted properly and I have no rubbing on the front derailleur in any gear. Once the chain came off from the bottom when my feet weren’t on the pedals (like I was pedaling backwards) but I couldn’t reproduce this by pedaling backwards.
I guess I can live with it jumping every other day, but I'm getting a little tired of wearing chain grease to the office. If you have some advice I’d gladly take it.
If what you describe happens only when shifting up front, the fix could be as simple as tightening the front derailleur's inner limit screw a half-turn, so that the chain isn't moved quite so far "in" during the shift to the inner chainring. But I bet you've already tried that.
Sounds like your bike is as much as ten years old, so it may not have all the original parts; that doesn't bode well. Higher-quality bikes got a whole lot more susceptible to chaos theory in the early to mid '90s; one slightly mismatched replacement part, like the proverbial butterfly flapping its wings, could throw off the whole drivetrain's performance.
I don't think the chain is the culprit; if it were, you would notice symptoms on the rear cogs much more than on the front chainrings. (An exception might be if you happen to have a nine-speed chain—narrower than necessary for your eight-speed cassette, and prone to wonky front shifting on chainrings that aren't spaced to match its lesser width.)
I think it's a chainline problem. That is, the bottom-bracket spindle—the rotating thing that the cranks attach to—may be too long, putting the chainrings too far "out," so that the chain is making unnatural angles in some gear combinations. (This wouldn't necessarily cause rubbing on the front derailleur.)
Some tests for you to perform: Is the chain more likely to jump ship when it's on the bigger (that is, the innermost) cogs in back? When you stand behind the bike and trace an imaginary line from between cogs 4 and 5 forward, does it line up between the two chainrings, or close to it? (A couple millimeters "in" or "out" won't matter much.)
You may need a bottom bracket with a shorter spindle. You can get them in a variety of lengths, but of course you need to know how long your current one is. Once you take the bottom bracket completely out, you'll see a sticker and/or a stamping that lists the spindle length. After the shorter spindle is in, don't forget to adjust the front derailleur's limit screws.