In a medium bowl, combine 2 tablespoons olive oil, 2 tablespoons lemon juice, garlic, oregano, salt, and pepper. Add chicken and marinate for 20 minutes.
Rinse quinoa under cold water. In a pot, combine quinoa and chicken broth. Bring to a boil, then reduce heat, cover, and simmer for 15 minutes until liquid is absorbed.
Remove quinoa from heat and let stand covered for 5 minutes. Fluff with a fork and stir in lemon zest and remaining 2 tablespoons lemon juice.
Heat remaining 1 tablespoon olive oil in a large skillet over medium-high heat. Cook chicken for 8-10 minutes or until the internal temperature reaches 165F (74C).
Divide lemony quinoa into four bowls.
Top each bowl with cooked chicken, diced cucumber, cherry tomatoes, red onion, feta cheese, and Kalamata olives.
Serve with a dollop of tzatziki sauce.