How to Make It
Place arugula, basil, pine nuts, garlic, lemon juice, salt, pepper, and 4 tablespoons of the oil in the bowl of a mini food processor; pulse until smooth, about 10 times, scraping sides of bowl occasionally.
Place zucchini, squash, and onion in a medium bowl; toss with vinegar, 2 tablespoons of the pesto, and remaining 1 tablespoon oil. Place chicken pieces in a separate bowl, and toss with 2 tablespoons of the pesto.
Preheat grill to medium-high (about 450°F). Thread chicken and vegetables alternately onto each of 8 (6-inch) bamboo skewers. Place kebabs on oiled grates; grill, uncovered, until chicken is cooked through and vegetables are tender and lightly charred, about 4 minutes per side. Serve chicken-and-vegetable kebabs with remaining pesto.