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Wash and dry produce.
Trim, peel, and cut carrots on a diagonal into ½-inch-thick pieces. Halve, peel, and cut onion into ½-inch-thick wedges. Trim and halve zucchini lengthwise; cut crosswise into ½-inch-thick half-moons.
Pat chicken* dry with paper towels and season all over with salt and pepper. Heat a drizzle of oil in a large pan over medium-high heat. Add chicken; cook until browned and cooked through, 3-5 minutes per side. Turn off heat; transfer to a cutting board. Wipe out pan.