First prepare the plum purée. Combine 1 cup dried plums and 6 tbsp of hot water in a food processor and process until smooth. Transfer to a measuring cup and set aside.
Now, prepare the marinade. Combine ½ cup plum purée, ½ cup balsamic vinegar, ¼ cup olive oil, ¼ cup brown sugar, ¼ cup lemon juice, minced garlic, Accent seasoning, and salt and pepper. Whisk until blended. Add chicken breasts to the marinade and pour into a sealed container. Refrigerate overnight (best marinated for at least 8 hours to tenderize).
Preheat the grill to 400 degrees F. While the grill is preheating, prepare the basting sauce.
Finely chop the remaining ¼ cup of prunes and place into a small saucepan. Add 2 tbsp of balsamic vinegar, 2 tbsp sugar, 2 tbsp plum purée, 2 tbsp lemon juice, and 1 tsp of garlic powder. Cook on medium heat until the mixture starts to bubble, then remove from the heat and stir in the butter. Set aside while you grill the meat.
Place the chicken, skin side down, and cook for 5 minutes to crisp the skin, then turn off one side of the grill (if using a gas grill) and place the chicken bone side down on that side to cook over indirect heat.
Cook on indirect heat for 30-40 minutes until the chicken reaches a safe internal temp of 165 degrees F. when tested with a meat thermometer. Baste with the BBQ plum sauce for the last 5 minutes of cook time.