Re: And they would have to sell the chickens to buy the food to feed them.
This also reminds me of one of the contributory factors in the great potato famines in Ireland. Smallholders lived off a subsistence diet of spuds while cash crops like grain were by and large exported.
Granted, in this case, the cash crop (chickens) are owned by the small farmers themselves rather than the landlords, but if your subsistence farming isn't going so well, those chickens are going to start looking mighty tasty. I won't be so churlish to point out the supply/demand side of things if suddenly everyone is selling chickens... (ok, I mentioned it)
It's a noble gesture at least, but I think you need to need to tackle both aspects (getting better/more reliable yields from subsistence farming and cash crops) at once.
Plus, how much research has gone into the particular breed of chicken being given out? I would hope that there's a pretty diverse selection (good, wide genetic pool) with particularly hardy breeds suited to the local conditions.