Yes Badgers can and will kill a chicken if they can get access to the chicken.
When badgers kill and take off with chickens they will usually get into the chicken coop at night and then remove one chicken at a time.
The badger will then usually return the next night and make off with another chicken and repeat the process every night or every other night until they remove and kill all of your chickens.
Badgers can tear holes through chicken wire and tear off wood panels that are not secured well so make sure you have the chicken coop secured really good at night.
You can use some hardware cloth over some chicken wire to help prevent the badger from getting into the chicken coops.
Badgers are also usually working alone and are very strong as well.