Preheat your oven to 400°F (200°C). Pat the chicken thighs completely dry with paper towels and season generously on all sides with salt and pepper.

Heat olive oil in a large, oven-safe skillet over medium-high heat. Place the chicken thighs skin-side down and sear for 5-7 minutes without moving, until the skin is deeply golden and crisp. Flip and sear for 2-3 minutes on the other side. Remove chicken from the skillet and set aside.

Reduce heat to medium. Add the butter to the skillet. Once melted, add the chopped shallot and sauté for 2-3 minutes until softened. Stir in the minced garlic and fresh thyme sprigs and cook for 1 minute more until fragrant.

Pour in the balsamic vinegar to deglaze, scraping up any browned bits from the bottom of the pan. Let it simmer and reduce for about 1 minute.

Add the chicken broth and blueberries to the skillet. Bring to a simmer and cook for 5-7 minutes, allowing the blueberries to burst and the sauce to thicken slightly.

Return the chicken to the skillet, skin-side up. Spoon some of the sauce over the chicken. Transfer the skillet to the preheated oven and bake for 15-20 minutes, or until the chicken is cooked through (internal temperature reaches 165°F or 74°C).

Remove from the oven and let the chicken rest in the skillet for 5 minutes before serving. Garnish with fresh thyme and serve warm with the pan sauce spooned over the top.