In a glass dish or a large sealable plastic bag, combine the tzatziki, garlic, oil and lemon juice. Add the chicken and thoroughly coat with the marinade. Cover the dish or seal the bag and refrigerate for 8 hours or overnight.
Preheat the grill, setting the burners to high. Oil the grate.
Place the chicken on the grill and cook for 15 minutes, or until fully cooked, turning halfway through. Season with salt and pepper.