This can be an opportunity to develop a positive relationship with neighbor through common interest. Proceeding to have third party intervention could be done more slowly. Clearly no need for speed since neighbors birds been doing their bit for a year now, at least.It is 100% your neighbors' responsibility to fence their chickens onto their own property.
If talking to your neighbor doesn't work and you still have problems then don't hesitate to contact Animal Control. People should not be over-sensitive about potentially offending people who have made it clear that they don't care about offending you.
