Most TV antennas are designed for 1.25" masts, but 10' would be the most you want on a chimney mount, especially if you have high winds in the area.
While very much more expensive, a 30' Rohn tower is a good choice for getting it up there a little farther without damaging the house.
While very much more expensive, a 30' Rohn tower is a good choice for getting it up there a little farther without damaging the house.