Prepare a 9-inch x 13-inch baking dish with non stick cooking spray. Place the chicken in the prepared baking dish.
In a small mixing bowl, mash 4 blackberries, using a fork, until completely muddled and the juices have completely released.
Mix the blackberries together with the brown sugar, vinegar olive oil, thyme, ¼ teaspoon paprika, garlic, cumin, salt, and black pepper. Mix until well blended.
Pour the blackberry sauce over the chicken. Sprinkle with the remaining paprika and additional salt and black pepper if desired.
Baked the chicken, basting often, for 40 to 50 minutes. Chicken is done when the temperature reaches 165 degrees F, in the thickest part of the chicken, on the meat thermometer.
Serve the baked chicken with additional blackberries if desired.