In a saucepan over medium heat, combine blackberries, balsamic vinegar, honey, olive oil, salt, black pepper, and thyme. Cook until the blackberries break down and the mixture thickens, about 10-15 minutes.

While the glaze is cooking, heat a skillet over medium-high heat. Season the chicken breasts with salt and pepper.

Add the chicken to the skillet and cook for about 6-7 minutes on each side, or until the internal temperature reaches 165°F (75°C).

Once the chicken is cooked, pour the blackberry balsamic glaze over the chicken in the skillet. Cook for an additional 2-3 minutes, allowing the glaze to coat the chicken.

Remove the chicken from the skillet and let it rest for a few minutes before serving. Drizzle with any remaining glaze.