In a medium bowl, whisk together 1 tablespoon olive oil, oregano, minced garlic, salt, and pepper. Add chicken cubes and toss to coat thoroughly.
Rinse quinoa under cold water. In a medium saucepan, combine quinoa and chicken broth. Bring to a boil, then reduce heat to low, cover, and simmer for 15 minutes or until liquid is absorbed.
Heat the remaining 1 tablespoon of olive oil in a large skillet over medium-high heat. Add chicken and cook for 6 to 8 minutes, turning occasionally, until the internal temperature reaches 165°F (74°C).
Fluff the cooked quinoa with a fork and divide equally among four bowls.
Arrange the cooked chicken, cherry tomatoes, diced cucumber, red onion, and Kalamata olives over the quinoa base.
Garnish each bowl with crumbled feta cheese and a drizzle of fresh lemon juice.
Serve immediately with a dollop of tzatziki sauce on top.