To prepare dressing, place mint and sugar in a food processor; process until finely chopped, scraping sides of bowl. Add vinegar, juice, salt, and pepper, and process 30 seconds to combine.
To prepare salad, combine chicken, cucumber, pecans, onion, and nectarines in a medium bowl. Drizzle dressing over salad; toss well to coat. Place 1 lettuce leaf on each of 5 plates; top each serving with 3/4 cup salad.
Note: In a pinch, substitute fresh melon for the nectarines. Look for chopped peeled melon in the produce section at the grocery. Cooking time is for the chicken.