Jane,
The best bet would be to thoroughly research the different cities/counties in Utah, as to who allows backyard chickens.
I saw this quote concerning Utah County...
19.04.235 Family food production.
Family food production means the keeping of not more than two cows, two sheep, two goats, twenty rabbits, fifty chickens, fifty pheasants, ten ducks, ten turkeys, ten geese and twenty pigeons, provided that an additional number of animals equal to two times the number listed above, and an additional number of fowl equal to five times the number listed above may be kept for each one-half acre of the lot over and above the minimum number of square feet required for a single-family residential lot in the zone, and provided that not more than three of the above-listed kinds of animals and fowl are permitted at any one time on any lot smaller than one-half acre. (Prior code § 22-1-6(30))
And another quote ~
8.01.190 Domesticated animals.
Domesticated animals means animals accustomed to living in or about the habitation of man, including but not limited to cats, dogs, ferrets and livestock. Domesticated animal, however, shall not include exotic animals. (Ord. 1461 § 2 (part), 2000)
So though chickens are generally labeled 'livestock', one can also argue that they are domesticated animals.
There are many large, cosmopolitan cities throughout the U.S. that now allow chickens. I would search as many names as you can and type them up onto a separate page to give if you ask the city council to rethink they're ordinance. Be prepared to give some general guidelines that other suburban cities are using, ie. six or less chickens, kept no closer than 20' from a building, no roosters, etc.
Research everything and then go to the council with a good defense. Ask your neighbors for letters of approval; you might want to also send out a petition in your neighborhood, asking for names/telephone numbers of people who agree that the city should allow chickens.
Good luck! And keep us updated.
Carla