In a very large serving bowl combine radicchio, endive, and kale. For dressing, in a small bowl stir together garlic, vinegar, mustard, salt, and pepper. Slowly drizzle in 1/4 cup oil, whisking constantly.
Season chicken on both sides with additional salt and pepper. In a large skillet heat remaining 1 tablespoon oil over medium-high heat. Add chicken; cook 2 to 3 minutes per side until done (165 degrees F). Place chicken on top of greens. Squeeze lemon over and drizzle with dressing. Sprinkle with Parmesan.