In a medium bowl, whisk together the balsamic vinegar, honey, minced garlic, Dijon mustard, dried thyme, salt, and pepper to create a marinade.
Place the chicken breasts in a large resealable bag or bowl and pour the marinade over them. Seal the bag or cover the bowl and marinate for at least 30 minutes (or up to 4 hours for deeper flavor).
Preheat the oven to 400°F (200°C).
Heat olive oil in a large oven-safe skillet over medium-high heat. Once hot, remove the chicken from the marinade (reserve the marinade) and add it to the skillet. Sear the chicken for about 4-5 minutes on each side until golden brown.
Pour the reserved marinade over the seared chicken and add the halved cherry tomatoes to the skillet.
Transfer the skillet to the preheated oven and bake for 20-25 minutes, or until the chicken is cooked through (internal temperature of 165°F or 75°C) and the tomatoes are tender.
Remove the skillet from the oven and let it rest for a few minutes. Sprinkle fresh basil leaves over the top before serving.
Notes
Marinate the chicken for up to 4 hours for deeper flavor.