as folks have mentioned, they kill chickens, eat eggs and spread diseases... and start fires! rats and chickens don't mix, they start out as a small problem and gradually become embolden and replicate once they find an open source of food which can be as little as simply having access to the chicken droppings.
any gap more than a half inch is enough for a female adult rat to get through and if they can get to food, they will turn that food into lots of babies, like upwards of 15 per litter, every 6 weeks. hardware cloth is a substantial up front cost but takes care of the issue once and for all. you could simply attache it to the fencing/frame you have now, using zip ties or the metal clips often used to secure the seams in various cages made of hardware cloth.