I would be concerned. Both rats and mice carry vermin and disease that could be carried to your chickens.
I have a mouse problem that I try to keep under control with traps so they don't attract snakes. Three times a rattle snake found its way into the run and had to be removed. Snakes are attracted to rats and mice.
I use the bucket trap as the mice have all caught onto the two types of commercial traps I used to use. The rodent climbs up a narrow ramp to the bucket, attracted to peanut butter on the revolving stick installed at the top, lose their balance and fall into the bucket to drown in a few inches of water. I've never had rodents catch onto this trap.
http://fivegallonideas.com/bucket-mouse-trap/ This video shows the bucket trap I made with a wood dowel, a piece of copper tubing, and some plastic sleeves over the dowel so the copper tube rolls. But you can buy the roller on the internet.