Step 1: Pat chicken breasts dry with paper towels. Season generously with salt and pepper on both sides.
Step 2: In a shallow dish or zip-top bag, combine 1 tablespoon olive oil, lemon juice, lemon zest, minced garlic, and half of the chopped fresh basil. Add chicken breasts, ensuring they are well-coated. Marinate for at least 20 minutes at room temperature, or up to 2 hours in the refrigerator.
Step 3: Heat the remaining 1 tablespoon olive oil in a large, oven-safe skillet over medium-high heat. Add marinated chicken breasts (without overcrowding) and sear for 4-6 minutes per side, until deeply golden brown. Remove chicken from skillet and set aside.
Step 4: Reduce heat to medium. Add cherry tomatoes to the skillet and cook for 3-5 minutes, stirring occasionally, until they start to soften and burst. Gently crush a few with the back of your spoon.
Step 5: Pour in the chicken broth, scraping up any browned bits from the bottom of the pan with a wooden spoon. Bring to a gentle simmer.
Step 6: Return the seared chicken breasts to the skillet, nestling them among the tomatoes and sauce. Reduce heat to low, cover, and simmer for 8-10 minutes, or until the chicken is cooked through (internal temperature of 165°F / 74°C).
Step 7: Stir in the remaining fresh basil during the last minute of cooking. Serve immediately with your favorite sides.