Blend together Worcestershire sauce, brown sugar, ketchup, Cajun seasoning, and garlic powder in a large bowl. Place chicken into the bowl and coat thoroughly with sauce mixture. Cover and refrigerate for 8 hours to overnight.
Preheat an outdoor grill for medium heat and lightly oil the grate.
Discard marinade and grill chicken on the preheated grill until no longer pink and the juices run clear, 6 to 8 minutes per side. An instant-read thermometer inserted into the center of chicken should read at least 165 degrees F (74 degrees C).