How long have you had the chickens? Or is the neighbor the new addition? I agree with the others, both that the hen doesn't sound loud and that it doesn't matter what we think... it's the complainer neighbor. As long as you're not violating any ordinances, you may just want to tough it out until the neighbor gets used to the hen noises if you can.
We started with fowl about 6 months after we moved into our house. Our closest neighbor's house is at least 300 feet from where we built our coop (I'm a TERRIBLE judge of units of measurement so they could be farther away... probably are, we have a 6+ acre lot). Our neighbor wasn't happy about our fowl at first. We had guineas and chickens. He wasn't happy about our dogs either. We had a Coonhound and a red nose pitbull. He didn't like anything about us actually. He had been friends with our home's previous owner who passed away about 6 months before we bought the house. But his wife was friends with my mother-in-law so he never got hostile towards us. Just complained and grumbled.
Anyway, we eventually rehomed the guineas to a farm up the road. They roamed too much. The chickens stayed. The next year we got more chickens. And eventually ducks. Somewhere along the way the grumpy neighbor got less grumpy and we now seem to be on pretty good terms with him.
All that said, if you're not violating any laws, ordinances or regulations by having chickens, I don't know what your neighbor can really do other than complain. Hopefully he'll get used to the sounds of happy hens, realize he was being a turd by complaining and stop complaining.