Gather all ingredients.

Prepare kabobs: Combine olive oil, garlic, lemon juice, oregano, and salt in a large resealable bag. Add chicken, coat with the marinade, squeeze out excess air and seal the bag; marinate in the refrigerator for 2 hours.

Prepare sauce: Mix yogurt, cucumber, olive oil, vinegar, garlic, and salt together in a bowl. Refrigerate sauce for flavors to blend, 1 to 2 hours.

Soak wooden skewers in a bowl of cold water for about 15 minutes. Preheat an outdoor grill for medium-high heat and lightly oil the grate.

Remove chicken from marinade and thread onto the soaked skewers. Discard unused marinade.

Cook the skewers on the preheated grill, turning frequently until browned on all sides and chicken is no longer pink in the center, about 7 to 8 minutes per side.

Serve with tzatziki sauce. Enjoy!