Melt the butter in a saucepan over medium heat. Mix in the beer, steak seasoning, seasoning salt, and black pepper. Coat the chicken with this mixture.
Lightly oil the grill grate. Arrange chicken breasts on the grill. Cook for about 20 minutes, brushing frequently with the beer mixture during the last 10 minutes, until chicken is no longer pink and juices run clear. Discard any remaining beer mixture. Top chicken with green bell pepper slices to serve.