In a large mixing bowl, whisk together olive oil, oregano, salt, and black pepper until well combined. Cut your boneless skinless chicken breast into 1-inch cubes and add them to the marinade, along with the lemon zest, lemon juice, and minced garlic. Toss everything together until the chicken is evenly coated, then cover and refrigerate for 30 minutes to 2 hours.

While the chicken is marinating, grab a separate bowl and combine Greek yogurt, grated cucumber, and chopped fresh dill. Stir the mixture until well incorporated and creamy. Refrigerate the dip until ready to serve.

Preheat your grill or grill pan to medium-high heat—around 375°F (190°C). Soak wooden skewers in water for at least 30 minutes to prevent burning, if using.

After marinating, remove the chicken from the refrigerator and allow it to sit for a couple of minutes. Thread the chicken cubes onto your skewers, leaving space between each piece for even cooking.

Place the skewers on the preheated grill and cook for 6-8 minutes on each side, turning until golden brown and fully cooked. Check for a temperature of 165°F (75°C) to ensure juiciness.

Once cooked, transfer the skewers to a serving plate and serve hot alongside the creamy yogurt dip.