In a large pot of boiling salted water, cook potatoes for 8 to 10 minutes or until just tender. Add green beans; cook for 2 minutes more or until beans are crisp-tender. Drain; spread potatoes and beans out in a single layer in a shallow baking pan to cool.
For dressing, in a large bowl combine vinegar, lemon peel, lemon juice, mustard, honey, thyme, salt, and pepper. Add oil in a steady drizzle while whisking constantly. Place chicken in a resealable plastic bag set in a shallow dish. Add 1/4 cup of the dressing to bag. Seal bag; turn to coat chicken. Marinate in the refrigerator until ready to grill or up to 1-1/2 hours. Add potatoes, beans, and green onions to remaining dressing in bowl; toss to combine. Cover and chill until ready to serve.
Drain chicken, discarding marinade. For a charcoal grill, place chicken on the rack of an uncovered grill directly over medium coals. Grill for 12 to 15 minutes or until chicken is no longer pink (170 degrees F), turning once halfway through grilling. (For a gas grill, preheat grill. Reduce heat to medium. Place chicken on grill rack over heat. Cover and grill as above.)
To serve, arrange romaine leaves on a serving platter or divide among four dinner plates. Top with potato mixture. Slice chicken and add to potato mixture. Sprinkle with cheese and olives.