I had that happen last year and I waited about 2 days before I actually took the egg and held it in warm water. Now keep in mind I could see where the chickies beak was and I only held the egg part way in the water, away from the beak. I did this 4 to 5 times during the day and the little guy finally made his way out.
This year I had two that couldn't get out either. # 39 and 40 of 40 chicks.
The first one tried for almost 48 hours. I tried the water thing and it helped but he was really stuck and worn out. So, I finally cracked the shell to loosen it and removed some of it from his head. I left the rest of the shell on him and didn't help him much after that. He was finally able to get out. But he was very exhausted and I didn't think he would live because he wasn't even trying to get up after an hour. So, I got some medicated water with vitamins. (broiler booster) and I gave him a bit of the water with a syringe twice. I also left him in the brooder so he would stay nice and toasty. Well, it worked and he is doing well.
My last chickie couldn't get out of his shell either so, I did the same thing, cracked the egg and peeled a bit of it away. He did finally get out, but he has a deformed foot and a spraddled leg. So, I put a splint on the legs tonight and will put a shoe on his foot if needed to try to straighten out the toe. He is very active and doing well other than the leg and foot problem.
Helping chicks hatch is not a good idea but these ones were trying for so long that I figured they would die if I didn't do something.
I have noticed that some people wrap the egg in a damp paper towel. I am going to try that next time.
Good luck!!
