It could work, but if the area is too small you will have to constantly be planting. So you move them to section 1, while planting section 2, then move them to section 2 when the grass is ready, and plant section 1 again. That might work. If the pen is large enough or you have few enough birds then you may be able to rotate between three or four pens every so often and keep everything growing pretty well. Choose what you plant wisely, tough & invasive is what you want. Try weeds, too, Dandelion, and the such.
I think the rotational grazing is the best way to keep chickens if it is at all possible.