Place all ingredients in a saucepan and bring to a boil, stirring constantly. Reduce heat and simmer, stirring occasionally, until sugar is dissolved and all ingredients are thoroughly combined, about 10 minutes.
Remove from heat, cover and let sit for an hour, or refrigerate overnight before serving.
Simmer chicken breasts in water to cover, until cooked through and tender, about 20 to 30 minutes. Add onion and celery leaves to the coking water for enhanced flavor, if desired.
When chicken breasts are done, remove them to a cutting board or plate. When cool enough to handled, shred or chop the chicken and add the barbecue sauce.
Keep the mixture warm in a slow cooker, if serving buffet style.