1. Heat 1 tablespoon olive oil in a skillet over medium heat. Cook chicken breast in the skillet 10 minutes on each side, or until juices run clear. Remove chicken from skillet and shred. Return to skillet, mix in pesto sauce, and continue cooking just until sauce is heated through.
2. Place greens in a bowl, and top with chicken, bell pepper, cucumber, and onion. Drizzle with remaining olive oil, balsamic vinegar, and honey. Season with salt and pepper. Toss, and serve.