Season the chicken: Pat the chicken dry and season both sides with salt and pepper. This step helps the chicken brown and stay juicy.
Sear the chicken: Heat olive oil (and butter, if using) in a large skillet over medium-high heat. Add the chicken and cook until golden on both sides, about 3–4 minutes per side.
Remove to a plate; it will finish cooking in the sauce.
Sauté the garlic: Lower heat to medium. Add a bit more oil if the pan looks dry. Stir in the garlic and cook 30–60 seconds until fragrant, not browned.
Build the sauce base: Add tomato paste (if using) and cook 1 minute, stirring.
Pour in chicken broth and scrape up browned bits from the pan. Add tomatoes and a pinch of red pepper flakes.
Simmer: Let the tomatoes bubble and soften, 6–8 minutes. If using canned, simmer until slightly thickened and saucy.
Taste and add salt if needed.
Return the chicken: Nestle the chicken and any juices back into the pan. Cover and simmer gently 6–8 minutes, or until the chicken reaches an internal temperature of 165°F (74°C).
Finish with basil and acid: Remove from heat. Stir in most of the basil and a splash of balsamic or lemon.
The acid brightens the sauce and balances the sweetness of the tomatoes.
Serve: Top with remaining basil and a shower of Parmesan if you like. Spoon over pasta, rice, or polenta, or serve with crusty bread for dipping.