Sweet yellow clover - Picture source: http://bolincreek.org
Turning the soil right after the chickens have done there business will increase the fixed nitrogen in the soil and continue to add a rich layer of organic matter. The organic matter will continue to break down all winter and be ready for a spring planting.
You can see the difference in egg color. The big one from the grocery store and the other two pastured raised (probably pullet eggs). Picture Source: http://suvirsaran.typepad.com
Not only is it good for the soil, but this will add to the rich nutrient content of the chicken eggs. Getting a deep orange color to the yolk and a rich egg flavor. I love these symbiotic relationships. It benefits everyone, or thing.
"Good is the enemy of great."