When you say, you neighbours hate chickens, do you know why they hate chickens? Is your coop too close to their bedrooms that prevent them from having good sleep in the early morning? Is it the smell? The poop that attract flies or food that entice mice?
If it's the sound, do you know whether it's all day or just certain time of the day?
If it's reasonable request, like your chicken keeping has lead to detrimental effects of your neighbours lives, then you need to minimise/eliminate those effects. You need to find out which part of your chicken keeping bothers them. But if your neighbours have been unreasonable, like your chickens have lower their property values and make the area less prestige, then I would say touch luck to them. Sometimes, if you give unreasonable people an inch, they'll take a mile.