Bring a large pot of salted water to a boil. Cook the rotini according to package directions until al dente. Drain, rinse under cold water, and let cool completely.
While the pasta cooks, season chicken breasts with salt and pepper. In a skillet over medium heat, cook for 6-8 minutes per side until golden and cooked through (internal temp 165°F). Let rest, then dice or shred.
In a small bowl, whisk together pesto, mayonnaise, and lemon juice until smooth. Season with a pinch of salt and pepper.
In a large bowl, combine cooled pasta, chicken, cherry tomatoes, mozzarella pearls, and torn basil. Pour the dressing over and toss gently to coat evenly.
Cover and refrigerate for at least 30 minutes (or up to 4 hours) to meld flavors. Serve chilled, garnished with extra basil.