In a large bowl, combine chicken cubes, olive oil, lemon juice, oregano, garlic powder, salt, and pepper. Toss to coat evenly. Cover and marinate in the refrigerator for at least 30 minutes, or up to 4 hours.
While the chicken is marinating, prepare the tzatziki sauce. In a medium bowl, combine Greek yogurt, grated cucumber, minced garlic, chopped dill, salt, and pepper. Stir well to combine.
Thread the marinated chicken onto skewers. If using wooden skewers, soak them in water for at least 30 minutes before use to prevent burning.
Preheat your grill to medium-high heat or heat a grill pan over medium-high heat.
Grill the souvlaki skewers for 6-8 minutes per side, or until the chicken is cooked through and slightly charred.
Serve the Greek chicken souvlaki hot with the prepared tzatziki sauce, pita bread, and your favorite Greek salad.
Notes
For an authentic experience, serve with warm pita bread and a side of cucumber and tomato salad.