the point is would you make an official complaint or ask the neighbor in a mature manner to keep the chickens in their own yard?
This did happen to us. We asked the neighbor to come look at our problem with roaming chickens and a turkey. Upon refusing to do anything saying it was OUR problem, the next time they were in the yard I let a shot from the shotgun off which was a warning shot but it took that to get her serious about keeping them in her yard (and she used my easy fix). She also called the sheriff who paid us a visit and could only tell us to be careful as it was a legal shot!! Good chicken fences make good neighbors, haaaa!