Season the Chicken: Pat the chicken breasts dry with paper towels and season them on both sides with salt, black pepper, dried oregano, dried basil, and dried thyme.
Sear the Chicken: Heat the olive oil in a large skillet over medium-high heat. Add the chicken breasts to the skillet and sear for 4-5 minutes on each side, or until they are golden brown. Remove the chicken from the skillet and set it aside.
Make the Balsamic Sauce: In the same skillet, add the minced garlic and sauté for about 1 minute until fragrant. Add the balsamic vinegar, chicken broth, and honey to the skillet. Stir to combine, scraping up any browned bits from the bottom of the skillet. Bring the mixture to a simmer.
Cook the Chicken: Return the seared chicken breasts to the skillet, along with the halved cherry tomatoes. Cover the skillet and cook for an additional 8-10 minutes, or until the chicken is cooked through (internal temperature of 165°F/74°C).
Add Spinach (Optional): If using spinach, add it to the skillet during the last 2-3 minutes of cooking, stirring it into the sauce until wilted.
Serve: Once the chicken is fully cooked, remove the skillet from the heat. Garnish with fresh chopped basil if desired. Serve the balsamic chicken hot, with the sauce and tomatoes spooned over the top.