Locations of cyborg chickens
Wasteland 3's first cyborg chicken can be found in the Garden of the Gods. It's located north of the Burning Corpse Den, and to get it you'll need at least a level four Animal Whisperer. Once you have that, you just need to convince him and bring him back to the coup at Ranger HQ.
The next chicken is located in the Sans Luxe Apartment complex behind a locked door. To get in, you'll need to repair a nearby generator that requires a level five mechanic skill. Once you are able to repair the generator, the door will open and the chicken will wait in the room. This time, you will only need three points in the animal whisperer skill for him to follow you.
For the third Cyborg Chicken, you will need to go to Broadmoor Heights Church. There you will see a small room at the side of the main entrance. To enter, you'll need to press a button nearby, which should be on the far left of the main entrance. You will again need a level four Animal Whisperer to bring it with you.
The last cyborg chicken you'll need to find can be found in the Patriarch's Bunker under Broadmoor Heights. It is specifically located in the second room on the second floor of the building. As the last cyborg chicken, you should be prepared with someone with a level six stealth skill to enter the area and a level five animal whisperer skill to have the chicken follow you.
Once you've gathered all the chickens at Ranger HQ and progressed through the game, you should receive your new special companion. As a precaution, during your gatherings, be sure not to take unnecessary risks as they are likely to disappear and even die in battle.