Combine oil, basil, marjoram and salt in a small bowl and reserve 1 tablespoon of the mixture.
Coat both sides of bell pepper, eggplant, zucchini, tomato and onion pieces with cooking spray. Grill the vegetables, turning once, until soft and charred in spots.
Rub the tablespoons of reserved herb mixture on both sides of chicken and sprinkle with pepper. Grill the chicken until cooked through and no longer pink in the center, 4 to 5 minutes per side.
Meanwhile, transfer the grilled vegetables to a cutting board and chop into 1-inch pieces. Return to the bowl and toss with vinegar and the remaining herb mixture. Serve the grilled chicken with the ratatouille.