Chickens live around 5-10 years. The Colonel was already fully grown when Cayde-6 found him at The Farm. It's been five years since D2 launched, and if we assume that five years have also passed in-game and in the lore, then he should not be alive still.
-
Zavala replaced the chicken every time time it died, like a lot of parents do. Or else it’s the Final Shape…