Cook the penne in a large pan of boiling water for 10 minutes until al dente. Drain and toss together with the pesto.
Meanwhile, heat the oil in a large pan, add the courgettes and cook for 5 minutes until softened. Add the pesto-coated pasta along with the chicken and tomatoes. Season with freshly ground black pepper and toss to combine.
Divide between bowls and garnish with the Parmesan shavings.