Prepare the Marinade/Dressing:
In a large mixing bowl, whisk together olive oil, lemon zest, lemon juice, red wine vinegar, minced garlic, oregano, salt, and black pepper until well combined.
Set aside half of the mixture in a separate container or mason jar for the dressing.
Marinate the Chicken:
Add the chicken breasts to the remaining marinade. Turn the chicken to coat thoroughly. Cover and refrigerate for at least 30 minutes (up to 2 hours for better flavor).
Prepare the Salad Vegetables:
While the chicken marinates, prepare your vegetables. Chop the romaine lettuce, quarter and slice the cucumbers, halve the cherry tomatoes, thinly slice the bell pepper and red onion. Place all vegetables (except avocado) in a large serving bowl.
Cook the Chicken:
Heat a cast iron skillet or heavy-bottomed pan over medium-high heat. Add a small amount of oil and a pinch of salt. Remove the chicken from the marinade (discard remaining marinade) and cook for 5-6 minutes on each side, until golden and the internal temperature reaches 165°F.
Rest and Slice the Chicken:
Remove the chicken from the pan and let it rest for 5 minutes. Slice it into strips or bite-sized pieces.
Assemble and Serve:
Add the sliced avocado to the vegetables just before serving. Add the sliced chicken to the salad, drizzle with reserved dressing, and toss gently. Serve with fresh lemon wedges on the side.