In a mixing bowl, combine the fresh blueberries, honey, thyme, olive oil, balsamic vinegar, salt, and black pepper. Use a whisk to blend until smooth.

Reserve a few tablespoons of the marinade for basting later.

Place the chicken breasts in a large resealable plastic bag or a shallow dish.

Pour the marinade over the chicken, ensuring it is well coated. Seal the bag or cover the dish and refrigerate for at least 30 minutes, or up to 2 hours for more flavor.

Preheat the grill to medium-high heat.

Remove the chicken from the marinade and discard the marinade used for marinating.

Place the chicken on the grill and cook for about 6-7 minutes on each side, or until the internal temperature reaches 165°F (75°C).

Baste the chicken with the reserved marinade during the last few minutes of cooking.

Remove the chicken from the grill and let it rest for 5 minutes before slicing.

Serve garnished with additional fresh blueberries and thyme, if desired.