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Dab chicken dry. Season with fair amount of sea salt and pepper and lemon zest; toss to coat. Heat 1 tablespoon olive oil and 1 tablespoon butter in 12-inch non-stick skillet over medium-high heat. Add chicken and cook 3 minutes; then flip and cook opposite side 3 minutes longer until chicken has cooked through. Set chicken aside.
Heat remaining tablespoon oil and butter in same skillet over medium-high heat. Add zucchini, then season with sea salt. Cook 4 minutes, tossing occasionally until just tender.
Return chicken to pan with zucchini. Drizzle in lemon juice and toss. Sprinkle with parmesan and parsley. Serve warm with more parmesan and lemon zest, if desired.