Do they cause problems? YES!
Dig holes, steal and eat chicks and eggs. They do carry disease and parasites. They also attract predators, such as fox, cat, snakes, and birds of prey.
I suggest putting out poison bait and keeping your chooks locked up tight until the poison is completely eaten. Then for the next few days, keep an eye out for dead and dying rats and dispose of them properly. After all that is said and done, you need to deworm ALL your animals.
Rats carry many of the same worms that affect dogs, cats, and chickens. Rats run through and defacate in feed and water, thus creating a world of infestation.
In between throwing rat poison out, I deworm my flock with ivomec in their drinking water. This way, not only are the chickens being dewormed but the rats that share their space and water.
-Kim