You never know with new neighbors, but I doubt 3 chickens would be a problem - especially when you’re allowed to have them. I think it’s best to try and keep a balance between being a good neighbor, and knowing your own rights.
It’s usually good to have open communication with your neighbors...
I think it’s great you’re thinking about your neighbors and being considerate. How about talk to the new neighbors, when/if they come. When you introduce yourself with those fresh eggs, as suggested by @3KillerBs, let them know they can talk to you if it’s too loud, etc.