Season the chicken breast evenly on both sides with sea salt, black pepper, and dried oregano.
Heat half of the olive oil in a medium skillet over medium-high heat.
Place the chicken in the skillet and cook for 6 to 7 minutes per side, or until the internal temperature reaches 165°F and the exterior is golden brown.
While the chicken cooks, slice the cucumber into half-moons and halve the cherry tomatoes.
In a small bowl, whisk together the remaining olive oil, lemon juice, and chopped fresh parsley to create a light dressing.
In a large salad bowl, toss the mixed baby greens with the cucumber and cherry tomatoes.
Drizzle the lemon-herb dressing over the greens and toss gently to coat.
Slice the cooked chicken into strips and place them on top of the greens.
Garnish with the sliced avocado and serve immediately.