Preheat the oven to 400°F. Place the chicken in a bowl and toss with ¼ cup of the pesto and salt and pepper to taste. Cover and marinate for 2-4 hours. Uncover, add the carrots, potatoes, onions, squash, and zucchini, the remaining pesto and additional salt and pepper, toss, and arrange on a foil-lined large rimmed baking sheet. Bake until the vegetables are tender and the chicken is cooked through, 35-45 minutes. Season with more salt and pepper and garnish with fresh basil.