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 2 TBS of basil vinaigrette.