It should be very possible to manage this situation, but it must be managed! Fencing first, and then taking the time to train the dog, and fencing.
Chickens are on everyone's menu, so having a safe coop and run for them is necessary, with or without this Beagle.
Training and fencing!
Mostly fencing, and he needs to be on leash out there, and lots of training.
He will stress the birds out, at least, and likely kill them, so stop this behavior immediately! Any dog needs to learn that the chickens are off limits, and it's harder for some than for others...