You could also rotate your grass or contain your chickens to a mobile chicken tractor and control where they forage, so as to not wear out one spot. To rotate, you fence off one side of the yard until it recovers from overgrazing, then switch pastures and repeat when necessary.
As for overseeding your existing grasses, this can get ticklish, as your native perennials and annual grasses are going to thrive more in your particular soil than any introduced species. So, you could conceivably grow the new grass for a season, maybe even two, then the original grasses will dominate anyway, as they do better in your particular growing conditions.
Better just to save yourself the money and time and develop the grasses you have already. If you have any access to composted material or even just fresh grass clippings, cover any bare spots in your grass with a 1/2 -1 in. layer of compost/clippings, fence it off to avoid further stress to the grass, water it well and let nature restore itself.
As for overseeding your existing grasses, this can get ticklish, as your native perennials and annual grasses are going to thrive more in your particular soil than any introduced species. So, you could conceivably grow the new grass for a season, maybe even two, then the original grasses will dominate anyway, as they do better in your particular growing conditions.
Better just to save yourself the money and time and develop the grasses you have already. If you have any access to composted material or even just fresh grass clippings, cover any bare spots in your grass with a 1/2 -1 in. layer of compost/clippings, fence it off to avoid further stress to the grass, water it well and let nature restore itself.