About nine (giving 10sqft run space per chicken), depending on how big your coop is. The rule of thumb is 4sqft of space per chicken in the coop (assuming there is a large run) and 10sqft per chicken in the run. Unless you plan to free range, then I think less is okay.
If they'd be contained the majority of the time, I'd say 9 or 10 max - run only, right? The coop is separate?? As the other poster suggested though, less birds means more space, which is always better.
Moveable coops can carry a higher count than stationary coops. A 6'x4' house with elevated roost can hold 15 chickens if used only for roosting. A open run area of 4sf per bird if it is moved every few days to fresh ground. It is not just size of coop, it is other management practices and fresh water and feed that can make a difference. Clean fresh ground, free of manure and mud, with fresh grass, bugs, weed seed, will keep your flock healthy and happy.