Pound and season the chicken: If using breasts, pound to an even 1/2–3/4 inch thickness for even cooking. Pat dry.
Rub with 1–2 tablespoons olive oil, 1 teaspoon salt, 1/2 teaspoon black pepper, and 1 teaspoon Italian seasoning or oregano. Let sit while you prep other elements.
Make the balsamic reduction: Add 1 cup balsamic vinegar to a small saucepan. Bring to a gentle boil, then reduce heat to a simmer.
Cook, stirring occasionally, until it thickens enough to coat a spoon, about 10–15 minutes. It should reduce by about half. Remove from heat.
The sauce will thicken more as it cools. If it gets too thick, whisk in a splash of warm water.
Preheat the grill: Heat a gas or charcoal grill to medium-high (about 400–450°F). Clean and oil the grates to prevent sticking.
Mix the bruschetta topping: Dice the tomatoes and place in a bowl with 2 tablespoons extra-virgin olive oil, 1–2 minced garlic cloves, 2 tablespoons finely chopped red onion or shallot, 1/2 teaspoon salt, and a pinch of black pepper.
Add a squeeze of lemon if you like. Stack basil leaves, roll them up, and slice thin (chiffonade). Stir most of the basil into the tomatoes, saving a little for garnish.
Taste and adjust salt and acid.
Grill the chicken: Place the chicken on the hot grill. Cook, covered, 4–6 minutes per side for breasts, or 5–7 minutes per side for thighs, depending on thickness. Flip once.
The chicken is done when the internal temperature reaches 165°F in the thickest part. Transfer to a plate, tent loosely with foil, and rest 5 minutes.
Assemble: Spoon the fresh bruschetta topping over the warm chicken. Drizzle generously with the balsamic reduction.
Sprinkle with the remaining basil. Add shaved Parmesan or torn fresh mozzarella if you’re in the mood.
Serve: Pair with a simple green salad, grilled asparagus, buttered orzo, or crusty bread. For low-carb, try zucchini ribbons or cauliflower mash.