Yes Hawks will kill chickens including full grown adult chickens.
A Hawk which is also sometimes known as a chicken Hawk will try swooping down and taking chickens during the daytime.
When I was growing up on a farm with chickens my dad had to watch the chickens closely and sometimes would have to shoot and kill a Hawk because they would try taking off with the chickens and kill them for food.
Owls will also harm and attack and kill full grown chickens as well but the owls will mostly take the chickens or kill the chickens at night.
If you have a chicken coop you need to add a top to the chicken coop to avoid the hawk taking the chickens.