In a bowl, combine olive oil, honey, thyme, garlic, balsamic vinegar, salt, and pepper. Mix well.
Gently fold in the fresh blueberries, careful not to smash them.
Place the chicken breasts in a large resealable bag or bowl. Pour marinade over the chicken, ensuring each piece is well-coated. Marinate in the refrigerator for at least 30 minutes (or up to 2 hours for maximum flavor).
Preheat your oven to 400°F (200°C).
Heat a large oven-safe skillet over medium-high heat. Add a little olive oil, then remove chicken from marinade (reserve marinade for later) and sear each breast for 3-4 minutes on each side until golden brown.
Pour the reserved marinade with the blueberries over the seared chicken in the skillet.
Transfer the skillet to the preheated oven. Bake for 15-20 minutes or until the chicken reaches an internal temperature of 165°F (75°C).
Remove the skillet from the oven and let the chicken rest for 5 minutes to allow juices to redistribute.
Slice the chicken and spoon the blueberry sauce on top before serving.