I am not a game biologist so don't hold me to any of the things I am about to tell you. These are just my personal observations and views on hunting chukars.
The nesting period seems to be similar to pairing as far as timing between the huns and chukars. The huns tend to nest two to three weeks earlier than chukars. The huns are normally nesting early April to early May while the chukars are late April to mid May. Both prefer dry open slopes, although the hun tends to pick flatter spots for their nests.
Chukars will fly individually at two weeks but usually don't fly as a covey until approximately four weeks and that is done with the parents.
Although the huns tend to like the dense brushy cover, I've found that chukars prefer open hillsides unless they are hiding from predators flying above. Chukars have a harder time getting off the ground without running than a hun does. Maybe due to the fact that they are a little bigger body wise with the same size wings.
Early in the season hunters tend to hunt near watering holes or rivers. I've never found this necessary. Chukars will go as far as two miles to water and then feed there way back to wherever they want to go. But they will continue to use these watering sources until they are harassed away. It doesn't matter whether they are hunted on September 15th or October 15th, they will keep using these places until they feel it is not safe. The only thing moving an opening date from September to October will affect is the size and age of the birds.
I try and hunt as many different area as possible. I have over 50 good places to hunt chukar in Idaho and Oregon. Some areas are down one year and great the next. I try to never over harvest an area knowing that I'll be back again next year. Although chukar hunters don't have much effect on populations it is possible to over hunt an area especially the easy to get to ones.
Predation doesn't have much effect on chukar and hun populations either. I have, however, seen Coopers hawks that are quite deadly on chukars. One chukar can fill a Coopers hawk belly for several days.
Idaho has a limit of 8 chukars and 8 huns in one day while Oregon has a limit of 8 which includes both chukar and huns. That makes a day in Idaho a little more desirable.