This dish is a great way to use up a bumper crop of tomatoes and herbs. Tender fresh linguine works well with the pesto, but you can use dried pasta as well.
Cook pasta according to package directions in a large Dutch oven, adding salt once water comes to a boil. Drain pasta, reserving 1 1/2 cups cooking water.
Wipe Dutch oven clean, and add olive oil. Heat oil over medium-high. Add tomatoes to hot oil, and cook, stirring often, until slightly softened, about 2 minutes. Add shallot, and cook, stirring often, until softened, about 2 minutes. Stir in garlic; cook, stirring constantly, 1 minute.
Add chicken, pasta, Fresh Herb Pesto, and 1/2 cup of reserved cooking water to tomato mixture, stirring to combine. Gradually stir in remaining cooking water, 1/4 cup at a time, until desired consistency is reached.
Transfer to a serving platter, and sprinkle with basil and mozzarella. Serve immediately.