I can understand them being frustrated about the barking dog. I can't stand listening to neighbors dogs go on and on barking, and they tend to automatically go on my dislike list....There's hardly anything more annoying than laying in bed when you have to get up early for work and hearing BARK, BARK, BARK, BARK, BARK.........but yeah that being said, I think you would probably be ok with your chickens as long as you don't have a rooster. They seem to be much, much more quieter than a dog. Would they even notice if you had a couple of chickens? Like, are they able to see into your yard?