In a medium bowl, whisk together olive oil, lemon juice, minced garlic, oregano, salt, and pepper for the marinade.

Add the cubed chicken to the marinade, toss to coat, and let it marinate for at least 15 minutes at room temperature, or up to 4 hours in the refrigerator.

While the chicken is marinating, prepare the yogurt sauce. In a small bowl, combine Greek yogurt, chopped dill, lemon juice, minced garlic, and salt. Stir well and set aside.

If using wooden skewers, soak them in water for at least 30 minutes to prevent burning.

Thread the marinated chicken onto the skewers, leaving a small space between each piece.

Preheat your grill to medium-high heat, or preheat your oven to 400°F (200°C).

Grill the chicken skewers for 8-10 minutes per side, or until cooked through and nicely browned. If baking, place the skewers on a baking sheet and bake for 20-25 minutes, flipping halfway through.

Serve the chicken skewers hot with the prepared yogurt sauce.