In a medium saucepan combine ketchup, water, cider vinegar, brown sugar, sugar, black pepper, onion powder, mustard, lemon juice, and Worcestershire sauce. Bring to boil, reduce heat and simmer. Cook uncovered, stirring frequently for 1 hour and 15 minutes.
While BBQ sauce is simmering place chicken breasts into a large pot. Fill with enough water to cover the chicken breasts. Bring to a boil and boil until chicken breasts are fully cooked. Remove from the pan and allow to cool for 10 minutes. Using 2 forks shred the chicken breasts.
Mix BBQ sauce with the shredded chicken and place onto hamburger buns. Top with coleslaw and dill pickle rounds.