Preheat a grill to medium. Cut four 12-inch-long sheets of heavy-duty foil. Drizzle 1 teaspoon olive oil into the center of each sheet.
Season the chicken with salt and pepper. Lay 1 piece of chicken in the center of each sheet and spread 1 tablespoon pesto on top.
Mound one-quarter of the zucchini, tomatoes and scallions over each chicken breast. Dollop 3 tablespoons pesto over each mound. Fold the foil over the chicken and vegetables; pinch the edges to seal.
Cover and grill the packets over indirect heat for 25 minutes. Remove from the grill and open carefully.