1. Add just enough water to skillet to cover chicken. Bring to simmering. Add chicken. Cover; simmer until cooked through, 15 minutes. Let cool completely. Tear chicken into thin strips.Prepare dressing:
2. Combine vinegar, mustard, shallots, salt and pepper in bowl. Whisk in oil in slow stream until well blended. Stir in cheese; set aside.To serve:
3. Arrange greens on platter with chicken, tomatoes and avocado. Top with bacon. Drizzle with dressing. Serve immediately.