That is Creeping Charlie. A highly intrusive ground rooting weed that will take over everything. If I were you I'd be out there with a strong mix of roundup and spray until that stuff was long gone. Even one viable root will take over the whole area. I somehow got some in some purchased plants and now I have to continually treat to get rid of it. Kill it out as best you can then reseed with something that is fast growing but not invasive. The chickens won't eat it. It isn't toxic in small amounts but is dangerous for kidneys and livers in larger amounts. It prefers shade so if you can get more sun to the area that will help keep it in check. I'd find a grass seed that does well in shade and reseed with that. Before chickens, I ran a landscape design business on the side. My true passion for most of my life. Unfortunately my spinal issues have stopped almost all of my garden
Well Crap what do I now won't round up hurt my chickens when they go outside in 2 months? My entire back yard is covered in this and it is fully shaded and most of my backyard is in a flood plane except where I have my chicken run.