Dice chicken into bite-size pieces. Halve the cherry tomatoes. Mince the garlic. Chop the basil and reserve a small handful for garnish. Season the chicken with salt and pepper.

Bring a large pot of salted water to a boil. Cook pasta according to package directions until al dente. Before draining, scoop out and reserve 1/2 cup of the pasta cooking water. Drain the pasta.

Heat 2 tbsp olive oil in a large skillet over medium-high heat. Add the chicken in a single layer. Cook, undisturbed for a couple minutes, then stir occasionally until golden and cooked through, about 6–8 minutes. Transfer chicken to a plate if it cooks much faster than the vegetables.

Reduce heat to medium. Add the minced garlic to the skillet and sauté about 30 seconds until fragrant. Add the halved cherry tomatoes and most of the chopped basil. Cook until tomatoes start to soften and release juices, about 2–3 minutes.

Add the drained pasta to the skillet and toss to combine. Pour in reserved pasta water a little at a time until you reach a saucy consistency that coats the pasta. Stir in the balsamic vinegar and grated Parmesan. Taste and adjust salt and pepper.

Plate immediately and top with the remaining basil leaves and extra Parmesan.