Prep the chicken: Pat the chicken dry. If using breasts, slice them into even cutlets about 1/2-inch thick. Season both sides with salt, pepper, and oregano.
If you want a lightly golden crust, dust each piece with a thin layer of flour.
Warm the pan: Heat a large skillet over medium-high heat. Add 1 tablespoon of olive oil. When it shimmers, add half the chicken in a single layer.
Sear the chicken: Cook without moving for 3–4 minutes, until golden.
Flip and cook another 2–3 minutes, until just cooked through. Transfer to a plate and repeat with the remaining chicken, adding more oil if needed.
Sauté the garlic: Lower the heat to medium. Add the remaining olive oil and the sliced garlic.
Cook for 30–45 seconds until fragrant, keeping it pale—don’t let it burn.
Make the tomato base: Add the halved cherry tomatoes and a pinch of salt. Cook for 3–5 minutes, stirring occasionally, until the tomatoes start to burst and release their juices.
Deglaze: Pour in the chicken broth or white wine, scraping up browned bits from the bottom of the pan. Simmer for 2–3 minutes to reduce slightly.
Add vinegar and spice: Stir in the balsamic vinegar and red pepper flakes if using.
Taste and adjust salt and pepper.
Finish the sauce: Reduce the heat to low and swirl in the butter until the sauce looks glossy and slightly thickened.
Return the chicken: Nestle the chicken back into the pan with any juices. Spoon the tomato sauce over the top and warm for 2 minutes.
Herbs and serve: Turn off the heat. Scatter fresh basil (or parsley) over the top.
Serve with lemon wedges if you like a bright finish.