Add the chicken breasts to the 6-qt slow cooker in a single layer if possible.
Pour the 12-oz bottle of BBQ sauce, 3/4 cup Italian dressing, 1/4 cup brown sugar, and 2 tablespoons Worcestershire sauce over the chicken.
Cover and cook on LOW for 6 to 8 hours, or on HIGH for 3 to 4 hours, until the chicken is very tender.
Remove the chicken to a cutting board or shred it directly in the slow cooker using two forks; stir the shredded chicken into the sauce to coat.
Serve the BBQ chicken on buns, over nachos, on baked potatoes, or on salads as desired.