Place chicken in a shallow glass dish and add in oregano, lemon juice, olive oil, sea salt, and pepper. Toss to coat evenly, and well.
Allow to marinate for a minimum of 30 minutes - or overnight, covered well - refrigerated.
Preheat a large skillet or grill on medium-high heat and cook chicken for about 4 minutes per side, or until cooked through and no longer pink in the inside.
Meanwhile, in a small glass bowl, or jar, whisk all dressing ingredients, then refrigerate until ready to use.
In a large salad bowl, (or 4 separate serving bowls) arrange arugula, cucumber, tomatoes, onion, chicken, and olives - nicely.
Top with feta and drizzle dressing over.
Toss to combine all ingredients just before serving.