Cut the chicken breast into 1-inch cubes and place them in a medium glass bowl.
In a small jar, whisk together the extra virgin olive oil, lemon juice, minced garlic, dried oregano, sea salt, and black pepper.
Pour the marinade over the chicken, tossing to coat every piece, and let it marinate in the refrigerator for at least 20 minutes.
While the chicken marinates, prepare the tzatziki by mixing the Greek yogurt with 0.25 cup of grated cucumber in a small bowl.
Thread the marinated chicken pieces onto wooden or metal skewers.
Heat a grill pan or outdoor grill to medium-high heat and cook the skewers for 8-10 minutes, turning occasionally until the chicken is charred and cooked through.
In a separate bowl, combine the cherry tomatoes, 0.5 cup of diced cucumber, and crumbled feta cheese to create a simple Greek salad.
Serve the hot skewers alongside the salad, the prepared tzatziki, and half of a toasted whole wheat pita.