Season the chicken breast with salt, pepper, and dried oregano.
Grill the chicken over medium-high heat for 6-7 minutes per side until fully cooked.
Cook the quinoa according to package directions and let it cool slightly.
In a small bowl, whisk together the Greek yogurt, lemon juice, olive oil, and chopped fresh parsley to make the dressing.
Chop the grilled chicken, cucumber, and bell pepper into bite-sized pieces.
In a large bowl, combine the quinoa, vegetables, and shredded carrots.
Toss the salad with the yogurt dressing until well coated.
Top with the grilled chicken and serve immediately.