Tire Rubbing Against Chainstay
Assuming the wheel is good (is fully seated and centered properly in the dropouts and is true; if you spin it along its axis, there shouldn't be lateral movement) you shouldn't be running a tire that rubs on the frame. This can eat out the paint of the frame, the frame, and/or the tire. 

Try moving to a different tire (possibly a smaller one, like a 700x23) if the wheel is good. Remember that you need some space between the tire and the frame, since the bicycle flexes under load (damaged frames can flex more than the undamaged frame, so might be something to check up on).