Place garlic cloves in the bowl of a food processor or blender; pulse until minced. Add 1/3 basil leaves; pulse until fine. Add 1/2 cup olive oil; process until mixture turns light yellow with flecks of basil. Add 1/2 cup balsamic vinegar; process until just combined.

Place chicken breasts, 1 tablespoon salt, 1 1/2 teaspoons pepper, and puréed basil mixture into a large resealable plastic bag. Squeeze out excess air, seal the bag, and toss to coat chicken with marinade. Marinate in the refrigerator for 2 hours, or up to overnight, turning occasionally.

Preheat the oven to 300 degrees F (150 degrees C).

Brown chicken in a large skillet over high heat, 4 to 5 minutes per side; transfer to a large baking dish. Bake in the preheated oven until cooked through, 15 to 20 minutes.

Transfer chicken to a cutting board; slice into 1/4-inch strips. Return to baking dish to absorb cooking juices. Keep warm.

Meanwhile, bring a large pot of lightly salted water to a boil. Add penne and cook, stirring occasionally, until tender yet firm to the bite, about 11 minutes. Drain well. Stir in chicken and juices from the baking dish.

Thinly slice remaining 2/3 basil leaves; place in a large serving bowl along with tomatoes. Stir in remaining each 1/4 cup olive oil and balsamic vinegar; season with salt and black pepper. Top basil and tomatoes with pasta, sauce, and chicken; toss to combine.