Bring a large pot of salted water to a boil and cook the cheese tortellini according to package directions; drain in a colander when done.
While the pasta cooks, heat 1 tablespoon olive oil in a large skillet over medium-high heat.
Add the bite-size chicken pieces to the hot skillet and season with kosher salt and black pepper; cook, stirring occasionally, until browned and cooked through, about 4–5 minutes.
Place the drained tortellini in a large bowl, add the cooked chicken and halved grape tomatoes.
Stir in 1/2 cup basil pesto until the tortellini, chicken, and tomatoes are evenly coated.
Add the chopped fresh basil and taste; adjust seasoning with additional salt and pepper if needed.
Serve garnished with extra fresh basil and grated Parmesan, if desired.
