If you build the coop correctly you should have no problems; also only feed what the chickens will consume so there is not food left to attract rats. Also, it is important that if you keep the food outside it should be in metal containers, not plastic.
I took these photos of the coop I want to build which is larger than needed for 2 chickens. The chickens are secure inside and can be let out to work the garden to keep insects under control.
Rat's-eye view of standard poultry netting most people use; it will not keep a rat out.
Better to spend the money once and buy hardware cloth like this; pay attention to security when attaching the wire to the framework.
By the way, the owner of the coop in the last photo said that racoons are smart enough to open that type of 'thingy' and he was changing to a locking garden gate latch for better security.
