Without giving up any spots for chukar the river breaks of the Columbia, Snake and many of their tributaries hold birds. Chukar love rock structure but you will commonly run them out of there into open grass hillsides. That is where you will also get up huns sometimes. Huns seem to be on the tops, benches and sometimes in thickets in chukar country. You can also find huns in the open farm land of the Palouse, they seem to be much more versatile birds.
Chukar are not particularly a hard bird to find but its a hard hunt, up and down canyons, and covering rough terrain quickly. It is not uncommon to see dozens birds in a day some days maybe even a couple hundred. (Key word is see, not necessarily get a shot at or even get close to.) When you are chukar hunting, have your ears open, they will talk, particularly when you have busted up a few groups and the singles hold tighter.
I will also say that I hunt a flushing dog so my experience is a little different.
I personally have never gotten into quail while chukar hunting. But that is just me.