Bring a large pot of salted water to a boil. Add pasta and cook 1–2 minutes less than package directions for al dente. Reserve 1/2 cup pasta water, then drain.

While pasta cooks, heat 2 tablespoons olive oil in a large skillet over medium-high heat. Season chicken with salt and pepper. Brown in batches for 3–4 minutes per side until cooked through. Remove chicken and let rest.

In the same pan, lower heat to medium-low. Add a splash of olive oil if needed, toss in cherry tomatoes and cook for 1–2 minutes to soften.

Return chicken to pan, add cooked pasta, pesto, and 1/4 cup reserved pasta water. Toss vigorously for 1–2 minutes, adding more pasta water as needed until silky and cohesive. Stir in grated Parmesan and finish with lemon zest.