Will my dachshund hunt/kill a house rat?

I have a dachshund and he hunts chipmunks and squirrels, which are rodents.. do you think he would hunt a house rat, i have a log cabin and there is a rat in the walls, i can tell it's a rat because of how it walks around and how it gnaws. somehow it comes out and gets into the trash, i can hear when it walks out in the kitchen at night (it scratches at the floor) i am extremely terrified and am hoping when my dog sleeps with me in my bed if it came in the room he would kill it, do you think since he hunts these other rodents he will hunt the rat? thanks, and any tips would be nice.