01 - Pat the chicken breasts completely dry with paper towels. Season both sides generously with salt and freshly ground black pepper.
02 - Heat olive oil in a large skillet over medium-high heat until shimmering. Add chicken breasts and sear for 5 to 6 minutes per side until golden brown and cooked through, reaching an internal temperature of 165°F. Transfer chicken to a plate and tent loosely with foil to rest.
03 - Reduce heat to medium in the same skillet. Add chopped shallot and sauté for 2 minutes until softened and fragrant, scraping up any browned bits from the bottom.
04 - Add blueberries, fresh thyme leaves, chicken broth, balsamic vinegar, and honey to the skillet. Simmer for 5 to 7 minutes, stirring occasionally, until blueberries burst and sauce reduces slightly.
05 - Stir in unsalted butter until melted and sauce becomes smooth and glossy.
06 - Return chicken to the skillet, turning to coat evenly with blueberry-thyme sauce. Simmer for 1 to 2 minutes to heat through. Serve chicken topped with additional sauce and garnish with fresh thyme sprigs.