Yes a bald eagle will try for your chickens if they want to. I had a full grown bald eagle try to take one of my ducks off their pool less than 100 feet from my house. The next day it showed back up with 3 of its friends. My neighbors free range their chickens and experience regular losses to bald eagles. One day they came home and there was one standing on the ground in front of their chicken coop, staring at the door. I live near Puget sound in Washington and there are plenty of other things for them to eat, I think they are a bit lazy and go for the easiest catch.
My duck yard is now completely covered with netting and it has discouraged the eagle from my yard, although they still land in the trees and watch my property and the neighbors. When our chicks are ready for the move to their coop they will have a completely covered yard just like the ducks.