The owner is aware of a potentially dangerous animal, he's already informed the neighbors that the dog bites. The neighbor can't seem to keep the dog confined, the dog continually escapes a chain-linked fence, the existence of which may imply something about the neighbor's concern about the dog's potential. In my opinion, the dog made his last mistake if he threatens me or a member of my family. Think of a child or grandchild in the yard instead of yourself and replay the scenario!
I had this very same problem a couple of years back, a neighbor had a 100+ pound German Shepard who had been trained for police work of some kind, the neighbor was a prison guard. The dog was constantly loose and harrassing the neighbors and other dogs in the neighborhood, often getting into fights with the dogs. He would run up barking and growling if he found someone going to and from their car. My daughter and grandson were living with us and on one occasion, the dog harrassed the two of them. The police were called and I told them that if the dog ever showed up in the yard again I would see to it that it was the last time it happened. The responding officer said that I would be justified in killing the animal.
Each locale has its own laws, one of which is usually some sort of "leash law" outlining what a dog owner must do to confine his dog.