The mounting point will have had it's threads stripped / damaged. Last resort is drilling, but that will be a **** if the screw is spinning.
Personally, I'd get a screwdriver bit on an electric drill and spin it backwards at a reasonable speed whilst pulling at the chrome surround at the screw end. The pulling motion on the screw, plus the screw spinning might be enough to draw it out. Obviously you'll want to do some repair on it once apart!