In the Dallas city code: Article I. General
Sec. 7-1.1. Definitions
(13) DOMESTIC ANIMAL means:
(B) a dog;
(C) a cat;
(D) a ferret;
(E) any bird, other than one in the Falconiforms or Strigiforms Order, that is commonly kept as a human's companion;
(F) any "pocket pet," such as a mouse, hamster, gerbil, guinea pig, or rabbit, that is commonly kept as a human's companion;
(G) any fish, such as a goldfish or tropical fish, that is commonly kept as a human's companion; and
(H) any non-venomous and non- constrictor reptile or amphibian that is commonly kept as a human's companion.
(25) PROHIBITED ANIMAL means:
(A) a "dangerous wild animal" as that term is defined in Section 822.101 of the Texas Health and Safety Code, as amended;
(B) a margay, badger, wolf, dingo, elephant, hippopotamus, rhinoceros, non-human primate (other than a spider monkey or capuchin), crocodile, alligator, caiman, gavial, venomous amphibian or reptile, racer, boa (other than a red-tail boa), water snake, python (other than a ball python), hawk, eagle, vulture, and owl; and
(C) any hybrid of an animal listed in Paragraph (A) or (B) of this subsection (other than a dog-wolf hybrid).
Further, in Article VII. Miscellaneous.
SEC. 7-7.3. KEEPING OF ROOSTERS.
(a) In this section, ROOSTER means the male of the domestic fowl.
(b) A person commits an offense if he owns a live rooster on any premises within the city.
(c) It is a defense to prosecution under Subsection (b) that the rooster is:
(1) kept on premises upon which animal production is permitted under Section 51A-4.201 of the Dallas Development Code;
(2) being exhibited at the State Fair of Texas or at a special event conducted with written permission of the city;
(3) owned by a governmental entity or participating in a health, research, educational, or similar program conducted by a governmental entity;
(4) owned by a medical, educational, or research institution operating in compliance with all city ordinances and state and federal laws; or
(5) being held for slaughter in a slaughterhouse or meat packing plant operating in compliance with all city ordinances and state and federal laws.
(d) A person who owns a live rooster commits an offense if he:
(1) fails to confine the rooster at all times within an enclosure that is of sufficient height and strength to retain the rooster;
(2) confines the rooster in an enclosure that is wholly or partially located less than 20 feet from any adjacent property line;
(3) maintains the enclosure in which the rooster is confined in a manner that creates offensive odors, fly breeding, or any other nuisance or condition that is injurious to the public health, safety, or welfare; or
(4) allows the rooster to violate the noise restrictions of Section 7-7.4 of this chapter.
(e) For the purpose of calculating the distance requirement of Subsection (d)(2) of this section, the width of alleys, street rights-of-way, and other public rights-of-way will be used. The distance between a rooster enclosure and an adjacent property line must be measured in a straight line, without regard to intervening structures or objects, from the nearest exterior wall of the enclosure to the nearest property line. (Ord. 26024)
Seems to me that you can clearly keep hens, no problem