In my opinion, there is no such place that has no predators (I realize that Vicky said "next to no predators". Cities have rats and skunks and raccoon, not to mention both tame and wild dogs and cats. Some even have problems with coyote, and I've seen posts on this forum of some pretty large snakes that have ended up in people's chicken runs.. I agree that some of the "to leave open or closed" question would depend on the nature of your run, and how secure it would be to nighttime predators but if it were my chickens, I don't really see what is to be gained by leaving the chicken door open at night...well I guess sleeping in from time to time would be nice, but I have to get up to take the dogs out anyway. I would build adequate ventilation and close it so that I'd sleep better. I know some folks have doors that are attached to timers or solar powered that open on their own in the morning.
