We have a similar looking rodent here in Oregon that we call a digger squirrel. They're everywhere. Our chicken house (it's not a coop, it's a house) has a plywood floor but is built on concrete piers and rocks (bad idea) rather than a solid concrete footing and foundation. A mother digger squirrel moved under the house and had babies. We discovered them in the chicken house eating the chicken food. We don't own a gun other than a pellet gun and don't have the heart for killing squirrels anyway, so we set a have-a-heart trap and caught and relocated the mom and babies one at a time. Then another squirrel moved into the territory and after we caught him another moved in! All in all we caught and relocated 9 digger squirrels. So far nobody new has moved in.
I don't want them around the chickens because of any parasites/diseases they might carry and because they love to eat the chicken food. I wish the chickens were more territorial and would chase them away, but they don't. They do chase little birds out of their chicken yard!