Prepare the Chicken Marinade: Mix the chicken breasts with olive oil, oregano, salt, pepper, and garlic powder in a large resealable bag or bowl. Refrigerate and let the chicken marinate for at least 20 minutes or up to 8 hours to infuse the flavors.
Make the Salad Dressing: Combine the vinegar, garlic, oregano, salt, and pepper in a small bowl. Slowly whisk in the olive oil until the mixture emulsifies. Adjust the seasoning to your liking and set aside at room temperature to let the flavors meld.
Cook the Chicken: Heat a grill or grill pan to medium heat. Place the marinated chicken on the grill and cook for 4-5 minutes on each side, ensuring the internal temperature reaches 165°F. Once cooked, let the chicken rest for about 5 minutes, then slice into strips.
Assemble the Salad: In a large serving bowl, combine the chopped lettuce, halved cherry tomatoes, cucumber slices, avocado, olives with their brine, feta cheese, and red onion. Arrange the grilled chicken strips on top.
Finish and Serve: Drizzle the prepared dressing over the salad and toss gently to coat all the ingredients evenly. Serve immediately for the freshest flavors and garnish with extra feta or olives if desired.