Oregon, Washington, Idaho, Nevada and I've heard of them in No. California. The area you hunt them can be varyed. Very very steep hill's to flats and not so steep hill's. To hunt them on flat's, you hunt the river bottom's early and late. Late morning to late afternoon they are usually inroute back up the hill's. I have hunted them off horseback in some places but there are a lot of places you don't even want to walk much less ride a horse. One year I did a lot of hunting at Cottonwood bridge on the John Day River. The climb up was murder and at times I caught the bird's on the side going up and down. I recall shooting at one and sliding down the hill at the same time. The bird fell and landed, dead, about 400yds down the hill. That's about 30yds out and 400yds down! But that people associate that type of terrain with them is because they never start looking until they get there. They also are found in less hospitable country where the huns are more prevailent. Chukars are a great bird to hunt in the very steep country, but it's the country that drew me, not the bird. I could find the bird in much more accessable areas.
By the way, do not confuse the high mountain areas with treed forest's, they ain't there. These are open arid country birds. Lot's of rock and sage bruch and cheat grass. Rattle snakes ad little water although never to far from water. If you find them on a hillside, they alway's fly down hill. They also make a neat "chuk, chuk, chuk" sound when flushed. I'll try to get some photo's of the country later this week if it doesn't get to wet to get in.