Drain chicken, discarding marinade. Grill chicken on the lightly greased 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. Cut chicken into bite-size strips. Combine the carrots and jicama in a bowl. To serve, line 4 salad plates with the lettuce. Top with carrot mixture, cucumbers, chicken, mushrooms, green onions, and peanuts. Stir dressing; drizzle 1 Tablespoon dressing over each serving.