A guy who raises cattle told me they will literally eat the eyes and tongue of a newborn calf as its being born. They have to keep very vigilant during birthing season.
You can get permits to shoot them. I have a friend who raises sheep that was having a problem with them going after ewes having thier lambs. He shoots them and hangs them up in the trees for the other vultures to see. Cut down on his problem considerably.
I had black vultures take several of my hens before I figured it out. I came outside once to find one eating what was left of one of my hens it took, and another time saw one snatch one right in front of me and carried it off to the woods. So, yes, they will eat your chickens. I hate them.