Your ... hawk is there first for a predictable and easy to catch prey assemblage which is dominated by small rodents...
.... Chickens are targets of opportunity... I free-range with hawks hunting my place for smaller prey.... yet ...seldom loose [a] chicken...
Add the small birds and squirrels that are all looking for an easy meal and find that your chickens' food fills the freeloaders bellies nicely. In fact as centrarchid pointes out your chickens' food not only draws hawk bait in the form of birds and rodents but if your coops and runs are not also bird and rodent proof, they make a dandy safe haven from the 3 species of chicken hawks trying to eat the freeloaders.
The big exception is the Sharp Shinned or Blue Darter hawk (the smallest of the chicken hawks) who together with the Coopers hawk will carry off baby chickens like a zoo elephant eats peanuts, especially when they have young to feed.