Chain keeps 'exploding' off the big ring
 

So every time I have the chain on the largest chainring in the front, and I push hard at all on the pedals, it violently jumps off the chainring to the outside (right). As far as I can tell it doesn't matter what gear it's in on the cassette, it's done it on the smallest ring and the mid-large rings. I'm also pretty sure that the frond derailleur is adjusted properly as it shifts just fine between all gears in the front. I've had the bike (specialized allez) for probably 4-5 years and it's never done anything like this before. It seems to have a habit of doing it at the worst possible times, leaving me immobilized in the middle of busy intersections/etc.

buy a new chainring and chain..
other than that, go to LBS, show them. they can see the issue in action.

Check your high limit screw on the front derailleur. It may shift OK but still be moving too far to the right. It should be adjusted just enough to allow crisp shifts to the large ring and no looser. Set it by having your shifter set to the middle (inner for a double) ring and pull the exposed wire to shift while you make the adjustment by 1/4 turns. This will eliminate the shifter adjustment from confusing things. Tighten the adjustment until upshifts get sluggish and then loosen it gradually until they smooth out, then stop.

So the bike is 4 or 5 years old and this is a new behavior. I'm thinking that a bent chainring tooth or twisted chain are the most likely causes. A close visual inspection should reveal either problem. If it's a bent chainring tooth you many be able to bend it back with a small adjustable wrench. If it's a twisted chain, youll probably be wise to replace the whole chain.

+1,
Usually this is a sign of wear or damage. The FD isn't designed to keep chains on rings, only to shift them at low tension. You might also be having similar issues on other rings, but the bigger ringer acts as a catcher.

Id start by taking the FD out of the equation altogether by removing if the cage can be opened (some can, some can't), or if you have a reusable connector on the chain. The bike should ride fine as a 1x? with the FD. Now maybe you can observe what's happening, and maybe see the problem.

Just to eliminate it as a possibility, shift the rear to about the 3rd in, and sight down the chin like a rifle. It should be very close to straight, on the 3rd or 4th rear sprocket and outer chainring. If the cassette is noticeably outside of the chainring, that may be a factor, but I'm hoping that you don't have this issue.

If you can't eyeball an obvious cause, here's things to look consider.

If it seems to happen at the same place on the chainring each time (foot position is the same) then it's the chainring.

If it happens randomly, it might be the chain.
If it only happens under load, it's chain or chainring wear (or both), measure the chain for stretch, which should be below 1% (1/8" over 12"), co check by using a screwdriver blade to lift the chain away from the chainring at the 1/2 wrapped position (front of bike). You shouldn't be able to lift it away enough to see more tan 3/16" of daylight between the chain and sprocket. If you can, what may be happening is the high tension shifts the chain back on the sprocket, so the next tooth coming to engage bumps a roller instead of falling into the gap. That lifts the chain, and allows it to climb over the side.

I'd agree with the few comments and since the chain is already on the large ring its not the FD.
But I'd suspect a bent chain ring, tooth damage or the ring is just flexing enough to allow the chain to move off line.