Chicken Coop, if your town's zoning doesn't say anything that the zoning officer can tell you about keeping chickens then I would suggest to:
a. Call up the zoning person again, and suggest that you are planning to get some pet chickens and that the pet laws should apply -- maybe suggest that it is like getting a few canaries or parrots, except that they happen to be more useful. Let the zoning person know that you are planning to make sure that your chickens meet the other requirements for polite living in your area (noise, nuisance, etc.) and ask them to let you know if they have any concerns.
b. Let your neighbors know that you are interested in having chickens, and tell them a little about how you are planning to keep the chickens in line as "polite" neighbors in your neighborhood. Tell them that the chickens might make some noise, but no more than a dog or playing kids would. Let them know how you are planning to manage the chicken manure, and if they are gardeners, offer them some for your garden. If your neighbors have kids, offer to let them come over and say hello to the chickens (with parent supervision). Ask your neighbors that if they every have any concerns about your chickens, to please talk to you.
For both neighbors and zoning person -- by reaching out and starting the dialogue BEFORE you get the chickens, so that if they do have any troubles, they can come to YOU instead of complaining to someone else.
My local laws permit me to have chickens, but I still value the goodwill of my neighbors. If my neighbors were really upset about my chickens, I'd try to change what was upsetting them -- but if my immediate next door neighbors were really, really upset, I would get rid of my chickens. So far my neighbors have been great. Which reminds me -- that I need to check in with my neighbors about the start of the gardening season. If they want, I can loan them my chickens for a little slug & bug control before the garden is planted.