The neighbor's chicken might have been seen as an invader into your dog's territory.
My dogs acted more aggressive toward my chickens until I moved and just turned everyone out together in the fenced yard. I don't let the dogs around young chicks but they are fine with the hens and roosters and three of my dogs are pitbulls, three are labs, a pug, an australian shepherd mix, a sheltie, two huskey mixes, a rat terrier, a lab mix and a tan and black coon hound mix.