I thought of a different solution to the one everyone else is pitching. If you could loop the rope you might be able to get it around the tower (if the diameter of the tower is low enough, and if it's not it's a bit of an unusual tower), and then you can 'shimmie' down the tower, working around the rope as you do. I'd expect you'd have better odds doing this then splitting the rope.

If a part solution hadn't been given (tie the rope in a loop) then you might even be able to gnaw through the rope so you have it in two pieces - one to wrap around yourself as a harness so you can slide about as you work the rope down the tower. These solutions do assume that the diameter of the tower is consistent in both directions.

Although if it got thicker on the way down you might be able to loop slack into it higher up and then consume this as you descend.