In a large oven-safe skillet, heat 1-2 tablespoons of olive oil over medium heat. Add the shallots, garlic, and rosemary sprigs. Sauté for about 3-4 minutes until the shallots are soft and fragrant. Add the red grapes to the pan and cook for another 2-3 minutes until the grapes start to soften and release their juices. Remove the mixture from the pan and set it aside.
Pat the chicken thighs dry with paper towels. Season both sides with 1 teaspoon of salt and ½ teaspoon of freshly ground black pepper.
In the same skillet, add the chicken thighs, skin-side down. Sear for about 5-7 minutes until the skin is crispy and golden brown. Flip the chicken thighs and sear the other side for 2-3 minutes.
Return the sautéed shallots, garlic, rosemary, and grapes to the pan, spreading them around the chicken thighs. Drizzle the balsamic vinegar over the chicken and grape mixture.
Transfer the skillet to the preheated oven. Roast for 20 minutes, or until the chicken is cooked through and reaches an internal temperature of 165°F
Remove the skillet from the oven. Sprinkle with fresh rosemary leaves for garnish, if desired.