A couple of years ago, I managed to photograph this one at about 13,500 ft. on the tundra on Mt. Evans, easily 2000 ft. above timberline:
http://www.flickr.com/photos/rwolf/5334104977/
I was as surprised as you to encounter a chickadee up there. It was a day of strong winds and I figured the out-of-place bird was probably a migrant that had been knocked down by the conditions or was merely waiting on the ground among the rocks until the weather improved.
-- Ron Wolf
Palo Alto CA