Yes, use two threaded top races as a saw guide as fietsbob noted. I'd cut it for at least 42mm of stack even if your current headset has a smaller stack height. That way you have maximum flexibility if/when it becomes necessary to replace the headset: you can always use spacers to accommodate a shorter headset, but you're SOL if your headset is too tall for the steer tube.

And no, the chrome won't be an issue when you back off the races after cutting. You will want to de-burr the inside and outside with a file or grinder, though.