Killing Hawks for recreational purposes or just because you want to kill the Hawk is illegal due to the hawks being an endangered species.
However if the hawk is killing your chickens then you do not require any special permits to kill off the hawk when it's attacking your chickens or trying to take off with your chickens.
You have a right to protect your property and chickens from the hawk or any other wildlife so yes you can shoot and kill the hawk if it's harming your chickens or killing your chickens.
If you're having constant problems with hawks then you can indeed get a special permit that protects you from any legal problems should you need to shoot the hawks because they'll harming your animals or chickens.