I also didn't bother reminding the OP that lockrings have left hand threads, but I'm starting to think that it's possible we're giving him too much credit. (no offense intended to the OP).

He's been riding fixed for two years, and possible hasn't ever changed a sprocket. If a dealer installed the sprocket there's no reason for him to know or remember that the lockring is counter-threaded.

To the OP, before you chisel the ring in two, check that you're driving it to the right, opposite to the way you'd remove a sprocket.