If your dog doesn't have a solid stay command, I would work on that and other basic obedience commands and activities before attempting any of the following. Both activities were done with different dogs, though both had very solid basic training. Both dogs were well-exercised before each session. Please note that doing one activity does not necessarily mean the other does not need to be done. Neither of these dogs had done the other activity first.
(My dog calmly sniffing a pullet face to face. This picture was taken after training was accomplished.)
Face to Face:
I held a calm chicken in my arms and slowly brought the chicken close to my dog who was told to stay. As he relaxed, I moved closer. Once he was calm (still in stay) I put the chicken on the ground, hovering close in case he broke his command.
When he got a little anxious to meet the chicken, I commanded 'leave it' which he also knows as I use that when he has to wait for his food or a bone or something. He immediately returned his attention to me and I praised him softly (not excitedly as I didn't want to rev him up). I picked up the chicken and put her away for the day.
Next day I did basically the same thing, but my dog was not in stay when I had the chicken. He jumped up a little at first, but I told him 'leave it' again and he backed away. Once he backed away, I held the chicken closer to him so he could sniff. When he didn't attempt to eat her, I praised him calmly and put the chicken away.
With this success, I moved the chicken in a cage into the room. He could sniff the cage, but he was not allowed to touch the cage with anything else including licking or pawing.
After a few days of being in the same room under supervision, my dog decided that the chicken wasn't all that interesting after all and ignored her unless she was free. When free I still have to tell him to 'leave it' occasionally, but he obeys without question and they get along just fine.
When first introducing a dog to moving chickens in an enclosed run, be sure to have the dog on a strong leash and collar that will not break off if the dog lunges.
I brought my dog towards the chicken run with my dog in heal position. When he first saw them, he got excited, so I stopped and told him to sit. When he didn’t obey, I followed through by pushing his bum to the ground and repeated every time he broke position in his excitement.
I stayed there and waited until my dog got bored of the chickens and started to ignore them. When that happened, I moved forward. I continued to stay and move following my dog’s cues and after nearly half an hour, I had him sitting calmly beside the run.
The following day, I took the same steps, but it ended much quicker. With several sessions (about two weeks of daily exposure), also decreasing the amount of exercise my dog had and adding food to the chicken run to get them excited periodically, I finally took him to the run off-leash and, while he showed curiosity, he ignored them.
I never had a problem with that dog with the chickens after the training.
Just because the techniques described above worked with my dogs and with other dogs I have trained over the years, does not mean that it will work for you. Please contact a dog training professional in your area before attempting any introductions.