In a large ziploc bag, add chicken breasts, basil, oregano, minced garlic, olive oil, red wine vinegar, lemon juice, and salt and pepper and marinate in refrigerator for at least 20 minutes and up to 1 hour
Heat additional 2 TBS olive oil in a large skillet over medium high heat. Add chicken breasts to the skillet and cook, flipping once, until cooked through, about 3-5 minutes per side. Set aside, let cool, and dice into bite-size pieces
While chicken is cooking, wash and chop vegetables and set aside
Assemble mixed greens, chopped veggies, olives, feta cheese, and chicken into each serving dish and drizzle with basil vinaigrette.