Chickens like green plants. That is to say, they like anything growing in their range. The problem is their over eager, busy scratching feet. Any plant with a shallow, lateral root system is toast, and soon you will have a landscape rivaling Mars or the moon.
The secret is to select perennial cover crops that have deep root systems. These are typically "bunching" plants rather than "ground cover" plants. But it does require a period of unmolested existence to get them established so they won't be vulnerable to those industrious feet.
Last winter, I planted some cover crops, including native bunch grasses, on a bare area where I removed three dead pines. I mulched it with straw, and then installed a temporary plastic deer fence around it to keep the chickens off of it, and yes, the deer, too, until it was in full growth and glory. It only took about six months, and I was able to remove the plastic fencing.