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