Bring large pot of lightly salted water to a boil. Cook pasta according to package directions.
Working directly over a bowl with a vegetable peeler, peel thin lengthwise strips of carrots and zucchini. Stop when you reach the inner cores (which will not be used).
Add carrots and zucchini to pasta water 5 minutes before estimated cooking time is up. Drain pasta and vegetables over chicken in colander. Transfer to large bowl. Toss gently with pesto and salt until thoroughly combined. Garnish with tomato halves.