Poodles are retrievers, like labs. You should never trust ANY dog of any breed unsupervised around your poultry, with the exception of a well-trained LGD breed. (those breeds are selected to have lower prey drive for chasing - they act to defend)
1st step is that the dog NEVER has access to the birds off-leash until you have finished the training and he is trustworthy.
2nd step is that the dog doesn't have access to the birds when you aren't around to supervise. (this doesn't mean that you have to be right there but you have to be somewhere close enough to know what's going on)
You already know that he is excited with the chicks. Find the closest distance that the dog first notices the birds in the brooder. This might be in another room if he is one to constantly glance at the door. Put your dog on leash and get some extra special treats that he only gets for this work - bacon, grilled chicken (no spices!), hot dog chunks, etc. When the dog glances toward the birds, say his name and "leave it" If he looks at you, give him a treat - if he doesn't, give a light pop on the leash (think tap on the shoulder). When he looks at you reward him.
You can also teach him "watch me" the same way. You can practice this at random times though out the day. If you have a couple extra minutes while you're watching TV or whatever, just say his name, pause, "watch me" When he makes eye contact, then reward him. You can also (if you get in the habit of keeping a small treat in your pockets) catch him looking towards you say "watch me" and then reward. Or just praise him verbally.
Once the dog is reliably paying attention to you and the birds at a distance, move a little bit closer. If he absolutely blows you off, you're too close. Just back up a bit and begin again. Eventually you will be right amongst the birds. You can then start at a distance or with a long line (20' leash or so) and work from there. I never ever leave my dogs/chickens loose unattended together.
I don't even trust Rayden
I don't mean I constantly hover over the dogs when they are out with the birds, but I am in the area and aware of what they are doing. Think of it as a small child. Even though you've taught them not to play with matches, would you leave them alone in the house with matches scattered all over the floor?
The most important part of the training is to set the dog up to succeed. Don't give him a chance to chase the birds. Don't give him a chance to disobey.
ETA: The best thing about teaching "leave it" is that it works for everything. Drop something on the floor and don't want the dogs to touch it? "leave it" See dog running toward a snake? "leave it" Lots of training and work, but it pays off!
Of course, some dogs just can't be trusted off-leash. Period. They are just too focused on the birds. In that case, just confine the dog when the birds are out.