Season the chicken breast with half of the sea salt, black pepper, and dried oregano.
Preheat a grill or skillet over medium-high heat and cook the chicken for 6-7 minutes per side until the internal temperature reaches 165°F.
While the chicken cooks, dice the cucumber into bite-sized pieces and halve the cherry tomatoes.
In a small bowl, whisk together the extra virgin olive oil, lemon juice, remaining oregano, salt, and pepper to create the dressing.
In a large bowl, combine the cucumber, tomatoes, chickpeas, and fresh parsley, then toss with the prepared dressing.
Slice the grilled chicken into strips and serve it over the salad, finishing with a sprinkle of crumbled feta cheese.