I would argue that no number of unaugmented, non-sentient chickens will be able to overthrow a farmer and continue running the farm.
Firstly, the chicken's ancestors does not naturally behave as a pack animal, in fact, they will fight with each other when confined in close captivity, which necessitates that their beaks be partially cut off. This makes it extremely difficult for them to cooperate, which is necessary for them to be able to physically overpower a human farmer.
Secondly, even in the unlikely case that the farmer is somehow debilated and dies from a heart attack (for example) after being attacked by a chicken, they will still have to contend with the remainder of human society. Chickens cannot run a farm, and unless the chickens are willing to slaughter their own kind / sell their unfertilised eggs in the delivery truck, the farm will quickly fail to deliver on its production contracts, and the rest of the chickens will be taken away when the farm is inevitably foreclosed.