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I used to live in the Churchland area of Portsmouth. I had chickens, so I have a couple of questions and suggestions for you...
Are you allow by city code to have chickens?
People at the zoning office should be able to tell you. 
If you are allowed to have poultry where you live, obtain a copy of the city code. In fact, get a few copies. If anyone comes to the door to complain, show them the copy.  I lived where the "truck farms" had been located. My property was allowed to have eleven chickens. When somebody turned me in, a zoning officer came out. She said all was fine and to enjoy my FIVE baby chicks. I guess my neighbors must have gotten tired of hearing me sing to and about my "lucky birds".
If the city code doesn't allow chickens, I don't know how to help you change the code. Chickens make less noise than dogs. When is the last time you saw a headline about a child being mauled by a bird? There are whole threads here on BYC about how to get codes changed. Neighbors are best bribed with fresh eggs. 
If you are allowed chickens and someone is hassling you, get to know your animal control officers. Make sure they know you can have birds. Make sure you birds are well maintained. The better your birds are cared for, the more likely animal control is going to stand behind you. 
Please let us know how things turn out. Best of luck!