Pat the chicken breast dry with a paper towel and season both sides with half of the sea salt, black pepper, and dried oregano.
Heat a large skillet over medium-high heat with half of the extra virgin olive oil.
Place the chicken in the skillet and cook for 6-7 minutes per side, or until the internal temperature reaches 165°F and the exterior is golden brown.
While the chicken cooks, dice the cucumber, halve the cherry tomatoes, and thinly slice the red onion.
In a small bowl, whisk together the remaining olive oil, lemon juice, remaining sea salt, pepper, and oregano to create the dressing.
In a large bowl, combine the cucumber, tomatoes, red onion, and diced avocado.
Drizzle the dressing over the vegetables and toss gently to coat, then sprinkle with freshly chopped parsley.
Remove the chicken from the pan, let it rest for 5 minutes, then slice it into strips.
Plate the cucumber-tomato salad and top with the sliced chicken breast.