Whisk together lime juice, honey, vinegar, garlic, salt, and pepper. Drizzle in oil, whisking until thickened. Place 1/4-cup dressing in a shallow dish. Add chicken and marinate, covered, in refrigerator for 1 hour.
Heat grill to medium and oil rack. Grill chicken for 6 minutes per side, until cooked through, or broil for 5 minutes per side. Cool slightly, then cut into 1/2 inch-thick slices.
On platter, arrange mango, beans, bell pepper, jicama, lettuce, and chicken. Drizzle with remaining dressing.