The outer face on a triple wall chimney should not get past slightly warm to the touch unless the OP has a roaring fire. The sun sh8ining on it will bring the temperature much higher. I am sure he/she wants to hide the bright glare coming from a stainless chimney on a bright sunny day. Almost all the suggestions to date don't take into account that the chimney will be exposed to a wide variety of temps and weather, and can't be brought into a paint shop and then reassembled on the roof. A spotted chimney may look even worse than a consistently shiny chimney.

It happens that my triple-wall stainless steel chimney was in the category of producing glare. I chose to build/enclose the entire chimney in a wood-based simulated brick housing that from the ground looks like real brick, and does not reflect sunshine into any of my neighbors faces. I do have to paint the trim every 4-5 years, not a big deal.