In a medium saucepan, combine blackberries, balsamic vinegar, honey, olive oil, minced garlic, salt, and black pepper. Cook over medium heat until the blackberries break down and the sauce thickens, about 10-15 minutes.

While the sauce is cooking, heat a skillet over medium-high heat. Season the chicken breasts with salt, pepper, and thyme.

Add a tablespoon of olive oil to the skillet and cook the chicken for about 6-7 minutes on each side, or until fully cooked and golden brown.

Once the chicken is cooked, pour the blackberry balsamic sauce over the chicken in the skillet. Let it simmer for an additional 5 minutes, allowing the chicken to absorb the flavors.

Remove the chicken from the skillet and serve with the remaining sauce drizzled over the top. Garnish with additional blackberries and thyme if desired.