Cut foil into eight large pieces (about 14 - 16 inches long) and start four grill packets by laying them out double stacked in a plus sign shape. At this point, you can line them with parchment paper, if desired, by simply putting a single layer just on top of the foil.
Evenly distribute the chunks of chicken, zucchini, tomatoes, and mushrooms. Set aside.
To make the pesto, combine the basil, spinach, Parmesan, pine nuts, garlic, and olive oil in a small food processor and process until a smooth paste. Spoon over the top of each packet. Season with salt and pepper.
To seal the packets, carefully bring up two of the long sides of the foil so the edges meet at the center. Fold the two edges over together at least three times. Fold the remaining open edges up on themselves at least two to three times and crimp them together with your fingers.
Grill the packets for 8 - 9 minutes on each side or until the chicken is cooked all the way through (no longer pink in the center) and the veggies are tender. Serve warm with whole-grain pasta or couscous on the side if desired.
Foil is necessary to make the packets. Parchment paper is optional to line the foil.