Bring a large pot of salted water to a boil. Add pasta and cook according to package directions until al dente. Drain and set aside.
While the pasta cooks, heat olive oil in a large skillet over medium-high heat. Season chicken with salt and pepper, then add to the skillet. Cook for 5–7 minutes, until golden and cooked through. Remove and set aside.
In the same skillet, reduce heat to medium. Add garlic and sauté for about 30 seconds. Pour in the heavy cream and let it simmer for 2–3 minutes. Stir in the pesto and Parmesan cheese until the sauce is smooth and thickened slightly.
Return the chicken to the skillet and add the drained pasta. Toss everything together until well coated. If desired, stir in cherry tomatoes for a burst of freshness.
Serve hot, garnished with extra Parmesan and chopped basil or parsley.