Electric fence may be your only option.
Bear are a game animal, and the states make big money by selling liscences to hunters, so it is very unlikely that they will let someone just shoot a bear because it comes into their yard after chickens.
When I was working for the County Conservation Division back in Wisconsin, we worked with a guy who had honey bee hives that were being destroyed by bears. We helped him install a 4 wire electric fence around his hives to protect them. 4 wires so that during the fall, winter and spring, if there is snow on the ground (northern WI) then the bottom and second to top wire were disconnected from the charger, and connected to the grounding rod to make sure the bear was grounded as it tried to crawl thru the fence (snow will prevent an animal from being grounded and you need to be grounded to get a shock. This was a simple fence, 4 wires attached to 4 fiberglass fenceposts that extend 6' high, all attached to a fence charger, his was solar because it was out in the middle of nowhere, where the farm fields were. Since he only attended to his hives occationally, he would turn off the fence, disconnect two of the wires and climb through the fence, probably not an option for you.
Maybe the local conservation service would be able to at least help you figure out how to build an electric fence to keep the bear out. Contact the local county conservation office, or the state division that works with farmers or even the Natural Resources Conservation Service ( the NRCS is the federal program) and see if they can help you come up with a design that might work. These agencies work with farmers and I'm sure they have had to deal with bears.
If you use ribbon fencing ( the wires are woven into a flat plastic ribbon to make it more visible), peanut butter on the ribbon will get them to taste the electric fence!