If you see mice that's a good sign - it means there are no rats around.
If possible, try to raise your chicken hut onto concrete blocks or logs of wood or something - that discourages rats from nesting under your chicken hut and gaining access to it easily.
Keep food stored in a galvanised bin with a secure lid. They can get thought plastic. Think the bastards can even get through concrete
Try to put only enough food out for the chucks as they can eat in a day ... so there's none left in their feeder overnight. Even if you lock the feeder in the hut with the chickens overnight, rats will inevitably find their way in.
Do not throw more bread for the chucks than they can eat. Give them bread cut down into tiny bits so they can eat it OK and don't leave it for rats.
If you do see a rat, get something done about it straight away, don't procrastinate, because already by that stage (once they're making themselves visible) it means there is an infestation.
Good luck ... chickens are great!