Cook the pasta in a large pot of boiling, lightly salted water until just tender, about 8 minutes. While this occurs, heat the oil in a large skillet set over medium-high. Add the chicken and cherry tomatoes and cook, stirring, 3 minutes. Stir in pesto and cook 1 to 2 minutes more. Reduce heat to medium-low.
When pasta is cooked, drain well, reserving 1/2 cup of its cooking liquid. Add the pasta and reserved cooking liquid to the skillet; season with salt and pepper and toss to combine. Sprinkle servings of the pasta with Parmesan cheese and garnish, if desired, with basil leaves.