Try serving with warmed French bread.
Preheat grill to medium-high heat. Sprinkle chicken with salt and pepper. Grill about 5 to 6 minutes on each side, or until no longer pink in the center. Let cool, then cut into strips.
Make the dressing: In a large serving bowl, whisk the yogurt, mayonnaise, tarragon, and salt until well blended.
Add the melon, cucumber, and chicken. Toss gently to mix and coat. Serve at room temperature.