A similar approach to the one rharv suggests is to patch in the pg dynamics plug-in to the insert on the vocal track. If you un-check the compressor box and just use the expander/gate you can adjust it to cut out any noise under a certain volume. Try setting the ratio up full with the fastest attack and release, then adjust the threshold so you just hear the vox. Takes a bit of practice, but at least it's non-destructive if you get it wrong!

Hope this helps. ROG.