In a small saucepan, combine the blackberries, balsamic vinegar, honey, minced garlic, and a pinch of salt and pepper. Cook over medium heat, gently mashing the blackberries with a fork until they release their juices and the mixture thickens slightly, about 10-12 minutes. Remove from heat and set aside.
Preheat your grill or grill pan to medium-high heat.
Brush the chicken breasts with olive oil and season both sides with salt and pepper.
Place the chicken on the grill and cook for about 6-7 minutes on each side, or until the internal temperature reaches 165°F (75°C) and the chicken is cooked through.
During the last minute of cooking, brush the blackberry balsamic glaze generously over the chicken, allowing it to caramelize slightly.
Once cooked, remove the chicken from the grill and let it rest for 5 minutes.
Drizzle any remaining glaze over the chicken before serving and garnish with fresh thyme leaves.
Notes
Let the chicken rest before serving for better juiciness.