Cook rotini according to package directions until al dente; reserve 1/2 cup pasta water and drain.
Season chicken with salt and pepper. Heat olive oil in a large skillet over medium-high heat and cook chicken until golden and cooked through, 6–8 minutes.
Lower heat; add pesto, spinach, and cherry tomatoes to skillet. Stir until spinach wilts.
Toss pasta into skillet, adding reserved pasta water a little at a time to loosen sauce.
Stir in Parmesan and pine nuts if using. Taste and adjust seasoning, then serve with extra Parmesan.