Bring a large pot of salted water to a boil and cook the penne until al dente according to package directions, about 10–12 minutes.
Drain the pasta in a colander, rinse briefly with cold water to stop the cooking, and drain thoroughly.
While the pasta cooks, halve the tomatoes and chop the red onion; shred or cut the cooked chicken into bite-size pieces if needed.
In a large salad bowl, combine the drained pasta, cooked chicken, halved tomatoes, chopped red onion, and pesto.
Toss everything until evenly coated with pesto, then season with salt and pepper to taste.
Serve immediately or chill in the refrigerator before serving, as desired.