Bring the margarine, apple cider vinegar, Worcestershire sauce, and salt to a boil in a saucepan over medium-high heat. Stir until salt has dissolved, and add the chicken breast halves. Return to a boil, reduce heat to a simmer, and cook until the chicken is tender and no longer pink inside, about 30 minutes.
Preheat an outdoor grill for medium-high heat, and lightly oil the grate.
Grill the chicken breasts on the preheated grill until the skin is browned, lightly charred in spots, and shows good grill marks, about 5 minutes per side.
