If you have time, marinate the chicken in about 1/3 cup of Italian dressing for 3-4 hours. If not, just combine the 2 and let them sit for 10-15 minutes.
Get grill warming up while you heat the water for the pasta. Boil pasta in salted water according to package instructions.
Meanwhile, cook chicken on the grill alongside the zucchini. (You can either cut zucchini into spears for easy grilling, or cut it into smaller pieces and use a grill basket like I did. Depending on the size of your chicken cuts and zucchinis, the vegetables might take longer to cook than the chicken!) Chicken is done when it reached 165 degrees F. (I love my meat thermometer! No more dry chicken!) Sprinkle salt & pepper on the chicken. Brush both chicken and zucchini with more Italian dressing.
Drain pasta and transfer to a serving bowl. Pour in 1/4 cup Italian dressing and the grape tomatoes. Toss to combine. Add grilled zucchini. Just before serving, sprinkle Parmesan cheese over the top and serve alongside grilled chicken.