Roof Safety: how to clean gutters on high steep roof?
Do not tie off to a chimney. Ever. I've demolished chimneys by pushing on them. (And, parenthetically, the physics of what I think your proposing is exceptionally poor.)

Don't leave nylon baking in the sun under any circumstances. 

I'm not a fan of permanent anchors either, though they can be done properly (i.e., safe and waterproof). The downside to them is that you have to get there unprotected to clip in. 

I'd consider putting a rope over the entire roof. (Thin cord, tennis ball, tennis racket; tie thick cord to thin cord and pull; tie thick cord to something substantial on both sides of the house. If you choose to tie off to a vehicle, tie a bight around the steering wheel as a reminder.)

Among the benefits of the 'cord over the roof' approach is that you'll have protection as you climb the ladder. Just be sure you know when and how to switch the direction of the rope grab. (Hint: alpine butterfly knot at the ridge and a second tether for when you make the switch.)

Get training on how to self rescue if you slip off the edge and are left dangling. Or at least have a phone tethered to you. 

I'm a big fan of protected ropework, but you need to understand the entire system.