Cook pasta in plenty of lightly salted boiling water until al dente, following packet instructions. Drain, rinse under cold running water and leave to cool.
Cut zucchini into rounds. Roughly chop rosemary leaves. Combine zucchini, rosemary, garlic and 2 tablespoons olive oil in a bowl and leave for a few minutes.
Heat a nonstick pan over medium heat. Add zucchini mixture and cook until zucchini are golden brown, 5 to 10 minutes. Sprinkle with salt and pepper and transfer to a large bowl with the pasta. Add rocket and tomatoes. Stir gently to combine.
Whisk the balsamic vinegar, remaining 2 tablespoons oil, salt and pepper in a bowl until combined. Stir the vinaigrette into the salad. Finely chop the leaves of all the herbs and set aside.
Heat oil in a nonstick pan over high heat and sauté the chicken until golden brown, about 8 minutes. Season with salt and pepper.
Distribute pasta salad among serving bowls. Top with chicken and herbs and drizzle with lemon juice.