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.
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You forget the traveler blessed all life with a longer life cycle so it's possible chickens can live a long time What's more concerning is the change to pigeons digestive system and metablism, saint-14 keeps feeding those greedy sods and they haven't got fat or died of over eating