Prepare Thyme Vinaigrette. Brush chicken with 2 tablespoons of the vinaigrette; set aside the remaining vinaigrette until ready to serve.
Grill chicken on the rack of an uncovered grill directly over medium coals for 12 to 15 minutes or until chicken is tender and no longer pink, turning once halfway through grilling. (Or broil on the unheated rack of a broiler pan 4 to 5 inches from the heat for 12 to 15 minutes, turning once halfway through broiling.) Cut chicken into bite-size strips.
Meanwhile, rinse green beans with cool water for 30 seconds; drain well. In a large bowl toss together beans, cooked rice, artichoke hearts, cabbage, carrot, and green onion. Pour the remaining vinaigrette over rice mixture; toss to gently coat.
If desired, arrange lettuce leaves on 4 dinner plates. Top with the rice mixture and chicken.
In a screw-top jar combine 1/4 cup white wine vinegar; 2 tablespoons olive oil; 2 tablespoons water; 1 tablespoon grated Parmesan cheese; 2 teaspoons snipped fresh thyme; 1 clove garlic, minced; 1/4 teaspoon salt; and 1/4 teaspoon black pepper.