Bring a large pot of salted water to a rolling boil and cook the pasta according to package directions until al dente. Reserve 1/2 cup of the pasta cooking water before draining.
While the pasta cooks, season the chicken pieces evenly with kosher salt and black pepper.
In a large skillet, heat the olive oil over medium-high heat. Add the chicken in a single layer and sear for 6 to 8 minutes, turning occasionally, until golden brown and the internal temperature reaches 165°F (74°C).
Add the minced garlic and halved cherry tomatoes to the skillet with the chicken. Sauté for 3 to 4 minutes until the tomatoes begin to soften and release their juices.
Stir in the balsamic glaze and the cooked pasta. Toss thoroughly to coat. If the pasta appears too dry, add the reserved pasta water one tablespoon at a time until reaching the desired consistency.
Remove the skillet from the heat to prevent the cheese from completely melting. Gently fold in the fresh mozzarella pearls and the chiffonade basil.
Garnish with grated Parmesan cheese and serve immediately while the mozzarella is soft and the basil is fragrant.