Prep the Chicken: Trim any excess fat from the chicken thighs and cut the meat into 1½- to 2-inch chunks.
Make the Marinade: In a large bowl, whisk together the olive oil, lemon juice, red wine vinegar, garlic powder, oregano, thyme, salt, and paprika.
Marinate: Add the chicken to the bowl and toss to coat evenly. Cover with plastic wrap and refrigerate for at least 1 hour, preferably 6 to 8 hours for the best flavor. (You can also marinate the chicken in a zip-top food storage bag.)
Soak Skewers: If using bamboo skewers, soak them in water for at least 30 minutes to prevent burning on the grill.
Skewer the Chicken: Thread the marinated chicken chunks onto the skewers, packing them closely together (they should be touching, not spaced apart).
Preheat the Smoker: Set your smoker or pellet grill to 225–250°F and prepare it for indirect heat. Use a mild to medium wood/pellet blend that won't overpower the flavor of the marinated chicken, such as a blend with cherry, hickory, and maple (one containing oak for a more robust flavor).
Smoke the Chicken: Place the skewers on the smoker and cook for 1½ to 2 hours, turning every 30 minutes. The chicken is done when it reaches an internal temperature of 165–175°F. (We like the texture best around 175°F.) Use a reliable instant-read thermometer to check the doneness in the thickest part of the meat.
Rest and Serve: Let the chicken rest for 5 minutes before serving.
Serving Ideas: While the chicken smokes, prepare the tzatziki and any additional toppings (our favorite tzatziki recipe is linked at the start of this blog post). Serve the skewers on a platter with a sprinkle of crumbled feta, fresh herbs, and a side of tzatziki for dipping. Or, wrap the chicken in warm pita with tzatziki, red onion, tomato, cucumber, and more feta for a handheld meal.