Mix barbecue sauce, oregano, bay leaves, smoked paprika, salt, and pepper. Add chicken. Refrigerate at least 4 hours or overnight for best flavor. Remove chicken from marinade. Discard any remaining marinade.
Heat oil in large sauté pot or braising pan on medium heat. Add chicken; cook 5 minutes on each side or until chicken is browned. Add chicken broth, stirring to loosen browned bits in bottom of skillet. Add crushed tomatoes, celery, onion, carrots, and potatoes; bring to boil.
Reduce heat to low; cover and simmer 30 minutes or until chicken is cooked through (165°F internal temperature). Serve in a bowl.