It kind of depends on who you ask. The restrictions and protections for birds of prey came from the feather trade of the early 20th Century. The law, known as, "The Migratory Bird Act of 1918" protects all BOP's, de facto. There is no blanket allowance for killing them, if they are killing your livestock. So if you ask naturists or government agents, the answer is "Hands off!"
So, get to know the law, itself, of course. Merely asking on forums will get you all kinds of responses. This is from the Internet Center for Wildlife Damage Management, http://icwdm.org/handbook/birds/HawksOwls.asp :
All hawks and owls are protected by federal and state laws. There are cases, however, in which they can create public health and safety hazards or seriously affect a person’s livelihood.
Contact your local USDA-APHIS-Wildlife Services office first if you are interested in obtaining a shooting permit. The USFWS and state wildlife agencies may issue shooting permits for problem hawks and owls if nonlethal methods of controlling damage have failed or are impractical and if it is determined that killing the offending birds will alleviate the problem.
Permittees may kill hawks or owls only with a shotgun not larger than 10-gauge, fired from the shoulder and only within the area described by the permit. Permittees may not use blinds or other means of concealment, or decoys or calls that are used to lure birds within gun range. Exceptions to the above must be specifically authorized by USFWS. All hawks or owls that are killed must be turned over to USFWS personnel or their representatives for disposal.
In other words, the government has to tell you it's okay to kill them. It's a hard thing to prove, of course... both the threat and that your chickens are crucial enough to warrant the death of a precious BOP.
DO try deterrents wherever possible - there are a lot of them and they are preferable to killing a valued member of the natural food chain. When they work.
I cannot condone killing your owl, of course. But where it comes down to you or them, and all else has failed - well, do what you think you gotta.
Edited by Davaroo - 4/8/12 at 6:29pm