I worked at a vet clinic, and I would first open the dog's mouth and remove the bone if you can see it. Otherwise you should observe your dog, and if he shows any signs of distress, vomits, or has diarrhea, you should take him to your vet. You should not try to induce vomiting as the bone could cause damage on the way out. In general, your dog should be able to digest the bone just fine, but you should not feed these bones to your dog on purpose.
The main issues with a dog eating a chicken bone is the choking and the bone cutting up the dog's insides. As long as they got it down okay, feed the dog some white bread or another soft food that will go around the bone. Make sure he isn't choking or having bad bowel problems. If there is bleeding or your dog isn't eating anymore, make sure to bring them to a vet.