Preheat the oven to 450F. Line a baking tray with foil.
Use a spiralizer or peeler to turn the zucchini into zoodles or “noodles”. Place in a large bowl, and salt liberally. Let sit for 10 minutes to draw out excess moisture.
Add the chicken breasts to the tray with the cherry tomatoes. Top each chicken breast with a dollop of pesto, and drizzle with oil. Season with salt and pepper. Bake for 15-18 minutes, or until fully cooked.
Drain the zoodles and add to a large non-stick frying pan. Add the pesto, and cook on medium heat until warmed through, about 2 to 4 minutes.
Divide into 4 bowls, and top with the baked chicken and tomatoes.
Garnish with parmesan cheese, lemon zest, and basil.