Mine usually start in when they want out of their small enclosed run, which is 6:00am-6:30am.
Then they may make some noise if they see a neighbors cat or something. If it's before 8:00am, I'll go out and say "What - is - the - DEAL?!". This is sometimes enough to distract them.
Finally, when one is laying the other will often make a scene. Today, though, the one who laid came out and started in. It was late morning, though, so I didn't worry about it.
In the end, I don't know what you can do to keep them quiet, other than distract them. If it's really early, I might try to talk to them, or encourage them to scratch around, etc. If it's later, I usually check to make sure they're fine (if I'm home), but I know they're noisy when I'm away and that's just the way it's gonna be.
Like you, I live with close neighbors (the closest of which got 5 chickens yesterday - but that's for another thread), and I do worry about both the noise, and the "chicken" stigma. We don't really have loud dogs in our neighborhood, but all things being equal, I doubt the neighbors even care or notice our hens most of the time.
Good luck, and try to not let it bother you too much. The stress has driven me bonkers at times, but I'm learning to laugh it off when appropriate, and get them to be quiet when it isn't.
-Dave