Dropping a rope down the chimney probably would have worked.

I once had to get a cat out of the neighbor's fireplace. Still can't figure
our how it got in there--maybe tried to catch a bird, and fell in. The cat
was atop the damper, and had been there for days before we figured out where
the crying was coming from. It refused to come out, so we called animal
control. He had a cable-noose on a pole, and managed to get it around the
cat's neck, but the cat resisted, and pulling would have broken the cat's
neck. So he left. In the meantime, my cat wandered into the room--when the
cat in the fireplace saw my cat, it came down voluntarily, and went home.

So, you could say that my cat rescued the other cat.