Place the chicken in the slow cooker. In a medium bowl, whisk together the barbecue sauce, Italian dressing, sugar and Worcestershire sauce. Pour the sauce over the chicken. Cover and cook on low for 4 1/2 to 5 hours.
Remove the chicken to a cutting board. In a small bowl, mix cornstarch and chicken broth. Stir it into the sauce in the slow cooker. Cover and cook on high until the sauce is thickened and heated through (10 to 15 minutes). Meanwhile, use two forks to shred the chicken. Return the shredded chicken to the slow cooker and stir. Add additional barbecue sauce if more sauce is needed or desired. Cover and continue cooking on low for 45 minutes. Serve chicken piled onto rolls. Add pickles, if desired.
Nutritional information included here is for the pulled chicken only. Rolls and pickles and extra BBQ sauce are extra.
*The brand of barbecue sauce that you use can make a big difference in the flavor of the chicken. I like Sweet Baby Ray's!