Another thing to check - and it's not something common, but, I've had it happen....
Make sure the firing pin on the hammer is free to pivot. I had one that was sort of frozen in place and didn't pivot. Crud or something had built up on it.
I hit it with some #9 and a brass brush and scrubbed it good and freed it.
Since the gun is older and used, it's possible it was cleaned with WD40 and the WD40 has turned to varnish.
BTW - the finish is probably nickle not chrome.
Be careful with using #9 or anything else with ammonia in it to clean the gun.
Worst case is the ammonia will attack the finish. Less severe is the tendancy for the ammonia to turn it yellow.
I use Ballistol on all my nickle guns to clean them.