How to export green screen footage.

I recently shot on a green screen, i keyed it in after effects with keylight but
want to do color correction in FINAL CUT. when i export the video it comes out
with a black background instead of transparency so it doesn't allow me to
composite footage over the background so i can't color correct or do anything
because the clips with the black solid background are useless. how can i export
the already keyed footage so that i keep the transparency for the
background?????

Open the AE manual and look up alpha channel.
You will need to export form AE using the Animation codec.
Trying to color correct Animation footage in FCP is going to drive you nuts.

Can you export "Lossless with Alpha"?

Unless there's a specific reason you may have, you can do pretty much everything
you can do in Color also in Color Finesse included with AE. It's even 32bpc as
of CS3 and provides a simplified version of the full interface as standard
effects controls on the main interface. Relying on the FCP roundtrip seems the
long way round...