Combine first 6 ingredients in a shallow dish. Stir well; set aside. Combine chicken and buttermilk in a bowl; stir. Cover; marinate in refrigerator 30 minutes. Drain; dredge a few strips at a time in breadcrumb mixture, tossing to coat.
Coat a nonstick skillet with cooking spray. Add oil; place over medium heat until hot. Add chicken to skillet; cook 3 minutes on each side or until done.
Arrange 1 cup lettuce on each of 4 plates; divide chicken and beets among plates. Top with 2 tablespoons dressing and 2 tablespoons cheese.