In a medium bowl, combine the chicken cubes, olive oil, dried oregano, half of the minced garlic, half of the lemon juice, salt, and pepper. Allow to marinate for 10 minutes at room temperature.
Heat a non-stick skillet or grill pan over medium-high heat. Add the chicken and cook for 8-10 minutes, turning occasionally, until the internal temperature reaches 165°F (74°C) and edges are golden brown.
In a small bowl, whisk together the Greek yogurt, chopped dill, the remaining minced garlic, and the remaining lemon juice to create the tzatziki sauce.
Toss the diced cucumber, halved cherry tomatoes, and sliced red onion together in a separate bowl.
To assemble, divide the cooked quinoa equally into four bowls.
Add a portion of the grilled chicken and the vegetable salad to each bowl.
Top each bowl with a tablespoon of crumbled feta cheese and a dollop of the prepared tzatziki sauce before serving.