Chicken thighs work best with this recipe but if you prefer, you can substitute 4 chicken breasts for the 8 thighs.
Add olive oil to a large nonstick skillet while heating the skillet over medium-high heat. When oil is hot, add chicken thighs to the pan and sprinkle the tops with salt and pepper as preferred. When undersides are nicely browned (about 4 minutes), flip over and brown the other side (about 4 more minutes).
Pour in chicken broth, wine, and balsamic vinegar. Add thyme and stir. Sprinkle tomatoes over the top, cover the skillet, and reduce heat to low. Simmer until chicken is cooked throughout (about 20 minutes). Remove the lid, add fresh basil, and continue to simmer until the sauce has reduced a little (about 5 minutes more).
Serve chicken and tomatoes over steamed rice with some of the sauce poured over the top.