I have a Specialized Allez that has been converted to single speed. When I originally built it up the chain was taught. Yesterday, it fell of while crossing train tracks. The bike has vert drops so I figure that the slack must have come from chain stretch. How much can one expect a chain to stretch over ~1500 miles?

probably enough to cause the chain-falling-off issue. If it's the first time it's fallen off in 1500 miles, try just putting it back on and see if it falls of again (if it doesnt fall off for another 1500 miles it's not really an issue).

if it continues to fall off and becomes an issue, you might have something bigger at the root (maybe it's the chainring allignment with the rear, maybe it's an old chain, maybe you'll need a singulator)... luckily, none of these issues costs a whole lot to remedy.

-or-

YES! YOU HAVE A SERIOUS ISSUE! You should stop at this point and use this issue to purchase a new frame that has horz dropouts/track ends! These vert drops will NEVER work!

(whichever you want to hear)

How much do you like riding fixed and how much do you have invested the current wheel? Another option would be to drop $150 on a White Industries ENO eccentric hub so you could adjust your chain tension. It'd be that plus $15-$20 for spokes to rebuild your current wheel with that hub.

Yes, check your chainline as well. If you sight along it, it should make a nice straight-as-an-arrow run from the rear to the front. Otherwise it can be pulled off the cog.

Certainly don't ride with a slack chain. I once found myself face down in the middle of one of Boston's busiest intersections due to poorly timed chain toss.

If it is the chain then it seems like the simple thing would be to just buy a new chain.
Just a thought.

rulers are cheap. measure it.

1500 miles is beyond the lifespan of more than a couple chains out there.
Just get a new freakin' chain.

or you could run a phantom gear....or change chainrings...ramps and pins add to dropped chains

Yup, if you're using the original cassette, substituting the other cogs with spacers, then the chain will always be prone to falling off. The teeth are not high enough, and there're little ramps designed to lift it off onto the nonexistent next cog. A ss freewheel could remedy this.
Anyway, 1500 mi is quite a lot, so you can just srug your shoulders and buy a new chain.

i was gonna say new chain, but...

ooooo, phantom gear! that's an idea.

nothing like a chainring seemingly floating in the middle of your drivetrain to take up slack

yeah thats what im going to do on my conversion