Many people say it can't be done, but I have two dogs, both mixed with different breeds, different ages, genders and temperaments and both are perfectly behaved around my chickens and can even be left alone with them. I have had one of the dogs + chickens for 12 years and the other dog for 2 years. The fact that your puppy has tried to play with chickens does not mean he can't be trained, it just means he is a puppy!
I believe that with training, most dogs can be trusted around the chickens when supervised. Most people do not take the time to train their dogs properly. Most don't know HOW to train properly. I didn't either, even though I was a former vet tech and groomer. I took my dogs to inexpensive group obedience classes at my local animal shelter and this is where I learned to communicate with dogs. It takes time but it is so worth it. I can take my dogs anywhere with me, including hotels, airports, long trips in the car and they are very well behaved. Even non-dog people enjoy being around them.
However, you may not get to the point of being able to leave dogs with the chickens when unsupervised. If that is your goal, it will be a lot more work and it comes with obvious risks. I think I was lucky in this regard, especially because my older dog helped me train my younger dog by example.
I agree with several other posters - you must not let your puppy have the chance to make any mistakes with the chickens. Also agree with taking the puppy with you on chicken chores - on leash.
First, I would always keep puppy on the leash around the chickens. NEVER let the puppy put his mouth or paws near the chickens. Distract puppy from this and encourage good behavior with treats. For example, work on teaching him to sit while the chickens are around, reward him with treats. Any opportunity the puppy has to do something wrong can effectively un-do weeks of hard work on training.
Second, I highly recommend a group obedience class. It is how you learn how to communicate with dogs. It is not as obvious as it would seem. If you can't do that, ask your local animal shelter for advice on a good training book or CD. The classes are better because you can ask the trainer questions about any specific problems you are having. Some advice for training: first exercise your puppy, but not to the point of exhaustion. Just to the point where they are not acting hyper. Then do short 15-20 minute training sessions. then lots of rewards and love. Do this 2-4 times a day, if you're too busy then at least once per day, preferably twice. It is amazing how much progress can be made even with only 20 minutes per day (after exercise).
Some important commands to work on with your puppy, this is done when the chickens aren't around:
"leave it" - I trained my dogs this command with food. I can put food on the ground in front of my dog and say leave it, they will not touch it. In order for your puppy to learn not to chase/play/kill chickens, they must know this command. The command can be taught in steps, email me and I can describe it, but most obedience classes will cover this. A key point is not to use a command unless you are pretty certain puppy will obey. So, unless you have this command down, do not let puppy run free with the chickens and yell 'leave it' from across the yard. Practice this command once you have it down when you are around the chickens. Take treats with you. Walk by chickens, puppy goes to sniff, say leave it, when he looks at you (which he should be doing after some training), good puppy give him a treat.
"gentle" This can come months after learning leave it, as you only will want to use it when your dog can safely go near chickens without playing or mouthing them. I taught this command by getting my dogs to take treats and toys very gently out of my hand. Once I trusted my dogs near the chickens with the leave it command, I let them investigate the chickens a little closer, reminding them to be nice with "gentle".
"come" This is a simple command at first, but the more advanced command comes when you train your dog to come even if they are distracted. This is especially important if your dog gets to the point where they can be trusted with chickens when supervised, but not unsupervised. You may start experimenting with letting the dog off leash to test him out, but to do this without chickens being killed, you need to be able to stop them in their tracks. You first perfect this command on leash without distractions, rewarding with treats, then move to off leash, then off leash with distractions, like at a dog park or walks in the woods where there are critters to chase. Only when you are very confident that you have this down should your dog be off leash with chickens. You will be very happy when your dog is trained to come to you no matter what. Although my dogs are great with the chickens, they both chase other animals, but even if they find a deer to chase, I call them and they come to me.
Feel free to email me to discuss more. Good luck!
Colleen