and the wind takes the chimney!

You mean that there was a clay tile poking above the brick, right? And that 1/2 of that tile is gone, right? If that is the case, you should be able to hire a mason to remove that single tile and install another. Not sure what cost would be, but I'm sure you won't get away with less than a couple hundred. You should find out where the half tile went - i.e. if it when down your flue, and what that means for your flue setup. Hopefully it's sitting at your cleanout. I'd get on the roof and look at the rest of the top tile. The rest might be loose and worth knocking out before it falls in the flue. Let us know what you find. If you locate the missing tile and it did no damage, I don't see why you can't continue burning until you get if fixed (unless it violates code by being too short relative to roof, etc.). Cheers!

Hmmm...okay - I'm not familiar with a solid clay liner, I've only seen tiles. Someone else will be able to help - good luck! Cheers!

It's not a single piece all the way down. What NH_Wood means by "tile" is a rectangular section of clay liner. It's usually a couple feet long and each is mortared to the one below. A mason (or even a good chimney sweep) can easily replace it, if it's only the top one. Not so easily if there is more than one or two that are cracked.

Without actually seeing this myself, I would expect it's fine to use unless the broken piece(s) are somehow down inside and blocking the air flow up the chimney. If there is a way you can check for this, it would be good. If nothing is blocking the flow, I would go ahead and burn. First time, though, I'd build a small fire to test the draft and that way, if something is haywire, you won't have a big pile of wood starting to burn but only a very small one. Just use common sense. Good luck.