Preheat the oven to 375 degrees. Prepare a 9x13 baking dish with nonstick cooking spray. Place the chicken into the prepared baking dish.
In a mixing bowl, mash the 4 blackberries until completely muddled. To the blackberries, add the brown sugar, vinegar, olive oil, thyme, ¼ teaspoon paprika, garlic, cumin, salt and black pepper. Mix until well blended. Pour over the chicken.
Sprinkle the remaining paprika over the chicken. Add additional salt and black pepper over the chicken, if desired.
Basting often, bake the chicken for 40 to 50 minutes or until a meat thermometer reads 170 degrees at the thickest part of the largest chicken breast.
Serve the chicken with additional blackberries, if desired.