Make the chicken marinade. In a medium bowl, mix ¼ cup olive oil, garlic, 1 tablespoon red wine vinegar, 1 tablespoon dried oregano, dill, salt and black pepper. Add chicken and toss to coat. Let sit for 15 minutes or up to 4 hours.

Meanwhile, make the salad dressing. Mix shallot, Dijon, remaining 2 teaspoons red wine vinegar, remaining 1 teaspoon dried oregano, lemon zest, and lemon juice. Stream in remaining 3 tablespoons olive oil while whisking until emulsified.

Preheat a grill or grill pan to medium high heat. Remove chicken from marinade, letting excess drip off. Cook chicken until lightly charred and the thickest part reaches 165°F internal temperature, 5-6 minutes per side. Remove from heat and let rest for 5 minutes before slicing.

Place chicken over greens with feta, cucumber, tomatoes, red onion, olives and dill. Toss with dressing and serve immediately.