Oklahoma City has an ordinance which prohibits tatooing of fish and dyeing of birds (the term "bird" does not appear to be defined, although "fowl" are considered "animals". Since the prohibition against dyeing specifically applies to "mammals" and "birds" I am not sure that chickens fall in that category - even though the title of the ordinance refers to "animals)
§ 8-117. - Artificial coloring prohibited; transporting artificially colored animals prohibited.
(a)
It shall be unlawful for any person to dye or artificially color or cause to be dyed or artificially colored any mammal, bird, reptile, or amphibian, including wild and domesticated species or to bring or transport any dyed or artificially colored mammal, bird, reptile, or amphibian, including wild and domesticated species into the City.
(b)
It shall be unlawful for any person to tattoo any fish or to cause any fish to be tattooed or to bring or transport any tattooed fish into the City.
(c)
It shall be unlawful for any person to artificially color any fish or cause any fish to be artificially colored or to bring or transport any artificially colored fish into the City when the artificial coloring is a result of the injection of dyes into the fish through the use of needles or other invasive techniques.
(Ord. No. 23145, § 2, 10-3-06; Ord. No. 23464, § 1, 10-9-07)
§ 8-118. - Possession, sale, barter or gift of artificially colored animals prohibited.
It shall be unlawful for any person to possess, offer for sale, sell, barter or give away any dyed or artificially colored animal.
(Ord. No. 23145, § 2, 10-3-06)
I was unable to find a state statute that prohibits dyeing of animals (unless someone is able to successfully argue that it constitutes "cruelty").
When OKC's ordinance was challenged by a fish store owner in 2007, it was argued that changing the color of fish by a dye bath would not violate the ordinance, since it appeared focused on dyeing fish by injection. OKC apparently decided that there wasn't any way to tell if the fish had been injected with dye or dipped in dye and declined to clarify that dye baths would be acceptable.
edited because I didn't see Cuban's post and wanted to clarify that the ordinance I found is an OKC ordinance.