What is it about standard poodles? ;-) I have lost 2 chickens to my poodle.. My chickens are in a secure run with an electric fence around it to keep dogs and other things from bothering the chickens. I have lost 2 to the dog because the stupid chickens found a little spot to get out and ran into the dog. I have 4 dogs and only the poodle kills them. This is an obedience trained, rally titled therapy dog who just plan wants to kill these birds. Some dogs trained or otherwise can never be trusted to be with small critters.
My standard poodle also is a chicken killer. She just wants to catch them. Chickens don't really like that though. Lots of work on recall and drop on recall taught her to listen the first time when called. The issue used to be when my kids did not shut the door or my neighbor kids. The birds are all fenced for their protection. The only birds she could get to are the geese. She knows not to mess with Boris an increasingly hormonal gander.
Poodles are water retrievers/bird dogs. It is a part of them I guess. Lots of training and supervision.