Yes you can legally shoot and kill a Hawk or any other wildlife even those wildlife that are protected if the wildlife or hawk is attacking your chickens or other farm animals etc.
The law about shooting hawks and other wildlife only applies to those just shooting the wildlife for fun or just because they don't want them near there area.
But if you have a hawk or other wildlife attacking chickens or other farm animals or animals on your property then you can legally shoot the hawk or other wildlife if they're attacking your chickens or other animals.
You don't need a permit to do so and won't get into trouble if the hawk is attacking or taking off with your chickens.