Here's a description of a water powered door opener. I assume the electric timer could be put back at your house and run the hose from your house out to the chicken house.:
I have a one gallon plastic jug to close mine. A timer opens a 1/4" solenoid and water starts flowing into it through small tubing When it gets heavy enough it pulls the gate shut and hits a push button switch to turn off the water. A cheap gate latch catches and holds it closed over night. A small hole in the jug lets the water drain out. In the AM a lawn water timer turns on to put water in another jug to pull up on the gate latch and a common door spring opens the gate and the water timer shuts off after one minute and a small hole also drains this jug. The water goes into their trough so they always have fresh water. Mostly built out of old lawn mower pulleys and small cable and junk but it has worked for years.
Built my own using a 12v linear actuator to lift and close chicken door, 2 12v electronic timers (one for open and then other for closing, 2 relays, 1 small 12v battery, a solar panel to keep the battery charged, some 16gauge wire, aluminum 'U' channel from home depot so the door will slide nicely. The chicken door I used was an old plastic cutting board my wife gave me. Maybe have $100 in it total and some sweat equity. Had to do some research on the internet on the wiring. I never wired relays before. A guy on you tube had a diagram that I copied. Took me about 5 hours total to build and install. Unbelievably, it worked the first time around. The linear actuator is perfect, durable and smooth as silk. It is also designed for an outdoor environment. All othe electronics and the battery I mounted on a board to the inside of the coop to keep out of weather and also makes it easy to get to to adjust/change program times when needed. I am very happy with it so far. Would definitely recommend the setup to anyone. Linear actuator has its own limit switches which makes wiring much easier.
I plan on posting pictures soon and hopefully a short video.
This is a new door on the market but the design can't be beat! It uses a screw drive to raise and lower the door so no predator could possibly lift the door even if they could get a hand/paw or nose under the door!