Marinate the Shish-Kebab: In a bowl, combine olive oil, minced garlic, dried oregano, salt, and black pepper. Add the chicken to the bowl and toss to coat them evenly with the marinade. Let the meat marinate for at least 15 minutes, or longer if desired.
Prepare the Lemon Rice Soup: In a pot, bring the chicken broth to a boil. Add the rice and cook until tender, about 15 minutes. In a small bowl, whisk together the lemon juice and beaten eggs.
Take a ladle of hot broth and whisk it into the egg mixture to temper it. Then slowly pour the egg mixture into the hot soup, stirring continuously. Cook for an additional 2-3 minutes until the soup thickens. Remove from the heat.
Season with salt and black pepper to taste. Remove from heat and garnish with fresh dill, if desired.
Prepare the Greek Salad: In a large bowl, combine the cucumber, tomato, red onion, Kalamata olives, feta cheese, and beets. In a small bowl, whisk together the extra virgin olive oil, red wine vinegar, salt, and black pepper. Drizzle the dressing over the salad and toss gently to combine.
Grill the Shish-Kebab: Preheat the grill to medium-high heat. Thread the marinated chicken onto skewers, alternating with bell pepper chunks, red onion chunks, and cherry tomatoes. Grill the kebabs for about 10-12 minutes, turning occasionally, until the meat is cooked through and the vegetables are charred and tender. Remove from the grill and set aside.
Warm the Pita and Serve: Place a nonstick pan over medium heat. Warm the pita on both sides. Cut into wedges.
Serve the Shish-Kebab alongside the lemon rice soup, Greek salad, warm pita with hummus, and coconut water.