In a medium mixing bowl, combine lemon juice, 3 tablespoons of olive oil, salt, pepper, oregano, and honey. Whisk until smooth. Add the chicken and marinate, uncovered, at room temperature for 15 minutes.
Meanwhile, in a separate mixing bowl, combine the lettuce, cabbage, and parsley, tossing until combined. Set aside.
Preheat the oven to 400ºF.
Heat the remaining tablespoon of olive oil in an oven-safe skillet over high heat. Add the chicken, discarding the excess marinade, and cook until lightly seared on both sides, about 5 minutes total. Transfer the skillet to the oven and bake for 6 to 7 minutes.
Divide the warm barley between 2 bowls. Drizzle with some of the Simple Lemon Vinaigrette and toss to coat. Top with the lettuce mixture, radish, cucumber, and feta. Finish with more vinaigrette and serve with Pita Chips.