What kind of display do you want? led or lcd? size? or do you want to hook it up to a computer? perhaps automatic recording of lap times would be be a good thing?
there are several components to this. counter, display, trigger and, optionally, communication to PC. I doubt you will find a circuit that is 100% what you want, but you should be able to find some pieces that can be put together.
the counter/timer part is straight forward. there are tons of circuits out there. however, most of them only do HH:MM:SS. getting to milliseconds won't be that hard but may take some design work. It's doable with out a microcontroller but a lot easier with one (steep learning curve, though). there are several counter chips that could do what you want.
The triggering mechanisms are going to be tricky. how wide is the track? distance is going to be your biggest headache. I would try using a laser pointer on one side and a photo transistor on the other. carefull alignment of the laser is needed. It also needs carefull shielding of the PT (to avoid ambient ligth effects). I would also modulate the laser pointer (not sure if that's even possible with a cheap laser pointer) and look for that on receive side to improve error rejection. Here's one that might be adaptable **broken link removed** note that you can use seperate power supplies for the laser and the rest of the circuit.