Tender, wood-smoked chicken thighs marinated in white wine, lemon, garlic, and Greek spices, piled into warm pitas with cool tzatziki and crisp vegetables for a bright, savory Mediterranean bite.
Make the marinade: In a large bowl or gallon-size zip-top bag, whisk together olive oil, white wine, lemon juice, minced garlic, Greek seasoning, and sweet paprika until well combined.
Marinate the chicken: Add chicken thighs and toss to coat. Cover or seal and refrigerate for at least 4 hours, preferably overnight.
Preheat the smoker to 275°F, using a mild wood like maple or apple (or your preferred mild wood).
Prepare for cooking: Remove chicken from the marinade and stack on a trompo-style vertical spit, or thread onto skewers and place in a grill basket. Reserve remaining marinade for basting.
Smoke the chicken: Place on the smoker and cook until the internal temperature reaches 175°F, about 2 hours, basting occasionally with reserved marinade.
Rest: Remove from the smoker and let rest for 5 minutes.
Slice: Using a sharp knife, shave thin slices from the outside of the chicken stack or slice thighs thinly across the grain.
Assemble gyros: Fill warmed pitas with sliced smoked chicken, tzatziki, red onion, romaine lettuce, tomatoes, and cucumbers. Serve immediately.