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 cooked through, about 4–5 minutes.
Place the drained tortellini in a large mixing bowl. Add the cooked chicken and halved grape tomatoes.
Gently fold in the basil pesto until the tortellini, chicken, and tomatoes are evenly coated.
Stir in the chopped fresh basil and adjust seasoning with salt and pepper to taste.
Serve garnished with additional fresh basil and grated Parmesan, if desired.