Use two forks to pull meat off the bones and shred in large pieces. Discard bones and skin, if desired. Place chicken pieces in a medium bowl. Drizzle with 2 tablespoons of the vinaigrette. Toss well to combine. Let stand 10 minutes.
Meanwhile, toss lettuce, mint, and oregano with remaining 1/3 cup Greek vinaigrette. Arrange lettuce on a large serving platter.
Arrange chicken in center of greens. Sprinkle with cheese and olives. Garnish chicken with mint and oregano sprigs. Serve with lemon wedges. Makes 6 main-dish servings.