In a small bowl, combine ½ tablespoon olive oil, chili powder, lime zest, and a large pinch of salt. Rub the mixture onto the chicken breasts, coating well on all sides.
In a large pan, over medium heat, warm 1/2 tablespoon olive oil. Once hot, add ¾ the red onion, and cook until softened, approximately 5 minutes. Add black beans, cumin, oregano, and cook for another 1-2 minutes, until fragrant. Season with salt and pepper, to taste, and set aside. Wipe the skillet clean.
Add an additional ½ tablespoon olive oil to the now clean skillet. Heat over medium heat. Add the chicken and cook for 4-5 minutes per side, until cooked through. Remove to a plate, cover with foil and let rest 5 minutes.
Whisk together the lime juice, 2 tablespoons olive oil and half the cilantro. Season with salt and pepper, to taste.
Pico de Gallo:
Toss together the tomatoes, jalapeno, remaining red onion and remaining cilantro. Season with salt and pepper, to taste.
Chop the romaine heart, thinly slice the avocado, and thinly slice the chicken breasts.
Assemble the salad by plating the romaine, topping with the sliced chicken, black bean mixture, avocado slices, and pico de gallo. Drizzle with vinaigrette.