Good Housekeeping Magazine has this particular situation regarding wind chimes in this months issue. Peggy Post says:
Have a chat with neighbor. Say those wind chimes are lovely, but boy what a noise they make. I hate to ask but would you mind taking them down in the evenings? Reader response says: I'd live with it, but have my windows insulated. I'd ask them to replace their wind chimes with my gift of quieter ones. I'd tape the sound one night, let them listen to it and then ask if they'd remove chimes.