GSDs tend to have high prey drives....Is your dog well trained otherwise? LEAVE IT is a command you absolutely MUST teach the dog. If you can not successfully 100% teach the dog to recall (come back to you) and "LEAVE IT" 100% of the time with ANYTHING - then no I would never trust the dog with the chickens even under supervision - unless the dog is on leash in hand. If the dog is well trained, knows leave it and recall, you need to start now with a long lead outside the run, EVERY DAY for a half hour or an hour, and when not on a lead keep away from the chickens, cover the side of the run the dog can see them - cloth, tarp, anything so the dog can not see them when you are teaching and interacting with the two.
Lead in hand, (short first, then longer and longer) start off with a standard 5-6ft leash. stand the normal distance away from the coop (say dog is usually stationed 30-40 feet away start there) when she pays attention to the birds, tell her "LEAVE IT". When she pays attention to you only, reward the dog. keep this up every day 1-2 times a day. slowly make the lead longer, put a training lead on (usually 20 or 30 ft leash) and rehearse like shes off leash. if she runs at the chicken run, start over with lead in hand on that 20 ft so you can jerk her back. get closer and closer to the run and the chickens.
the dog has to learn that the chickens are not toys and ignoring them is what you want and expect of her. it will be a slow process, it can take months for a dog to learn. The important thing is when you are not outside and the dog is tied up or something, she doesn't need to be able to see the birds until she gets the hang of ignoring them. - if you don't take away the sight of them, shes just going to keep getting excited by their presence when shes bored.
Good luck. You may want to seek a professional's advice.