In a small bowl, whisk together the olive oil, lemon juice, sea salt, black pepper, and dried oregano to create the marinade.
Place the chicken breast in a shallow dish and pour half of the marinade over it, ensuring it is well coated. Let it marinate for at least 15 minutes.
Rinse the quinoa under cold water, then combine it with 0.5 cup of water in a small saucepan. Bring to a boil, then reduce heat, cover, and simmer for 15 minutes until fluffy.
Preheat a grill or grill pan over medium-high heat. Grill the chicken for 6-7 minutes per side, or until the internal temperature reaches 165°F.
While the chicken and quinoa cook, dice the cucumber, halve the cherry tomatoes, and finely mince the red onion and parsley.
In a large mixing bowl, combine the cooked quinoa, diced vegetables, and the remaining half of the marinade. Toss well to combine.
Slice the grilled chicken into strips and serve it over the quinoa salad, garnishing with fresh parsley.