Preheat your oven to 375°F (190°C).
In a large skillet, heat the olive oil over medium-high heat. Season the chicken breasts with salt and pepper, then add them to the skillet. Sear the chicken for about 4-5 minutes on each side until golden brown.
While the chicken is cooking, prepare the blueberry sauce. In a small saucepan over medium heat, combine the blueberries, balsamic vinegar, minced garlic, thyme leaves, and chicken broth. Stir gently and let the mixture simmer for about 5-7 minutes, or until the blueberries start to break down and the sauce thickens slightly.
Once the chicken is nicely browned, transfer it to a baking dish. Pour the blueberry sauce over the chicken, making sure to coat it evenly.
Bake in the preheated oven for 20-25 minutes, or until the chicken is cooked through and reaches an internal temperature of 165°F (75°C).
Remove the dish from the oven and let the chicken rest for a few minutes. Garnish with additional fresh thyme before serving.