"Chicken hawk" is a name given to what are actually Red-tailed hawks, because they've been known to kill chickens. Regardless of what they are called, it is illegal to kill them as they are consider a migratory bird. I don't know if "animal control" there is the same as our "game wardens" here, if so they should know it's illegal and shouldn't have advised you to kill the hawks. It's not law governed by State but on a Federal level.
Even though I agree with you that if a hawk is threatening a dog we should be allowed to kill them, it's still illegal and you might want to be careful.
§ 703. Taking, killing, or possessing migratory birds unlawful
How Current is This?
(a) In general
Unless and except as permitted by regulations made as hereinafter provided in this subchapter, it shall be unlawful at any time, by any means or in any manner, to pursue, hunt, take, capture, kill, attempt to take, capture, or kill, possess, offer for sale, sell, offer to barter, barter, offer to purchase, purchase, deliver for shipment, ship, export, import, cause to be shipped, exported, or imported, deliver for transportation, transport or cause to be transported, carry or cause to be carried, or receive for shipment, transportation, carriage, or export, any migratory bird, any part, nest, or eggs of any such bird, or any product, whether or not manufactured, which consists, or is composed in whole or part, of any such bird or any part, nest, or egg thereof, included in the terms of the conventions between the United States and Great Britain for the protection of migratory birds concluded August 16, 1916 (39 Stat. 1702), the United States and the United Mexican States for the protection of migratory birds and game mammals concluded February 7, 1936, the United States and the Government of Japan for the protection of migratory birds and birds in danger of extinction, and their environment concluded March 4, 1972 [1] and the convention between the United States and the Union of Soviet Socialist Republics for the conservation of migratory birds and their environments concluded November 19, 1976.
http://www.law.cornell.edu/uscode/16...3----000-.html