Add the garlic, oregano, rosemary, paprika, salt, pepper, olive oil, halal white grape juice (or broth), and lemon juice to a food processor. Blend until smooth.
Place the chicken into a large bowl. Add the bay leaves and pour the marinade over the chicken. Toss until every piece is evenly coated.
Cover and refrigerate for at least 2 hours or overnight for the best flavor.
Soak wooden skewers in water for 30–45 minutes.
Prepare the Homemade Tzatziki, vegetables, and any side dishes while the chicken marinates.
Thread the marinated chicken evenly onto the soaked skewers.
Heat an outdoor grill or grill pan over medium-high heat and lightly oil the grates.
Grill the Greek Chicken Souvlaki Recipe for about 5 minutes, turning frequently until evenly browned and the internal temperature reaches 160°F before resting to 165°F.
Lightly brush the chicken with the remaining marinade during grilling, then discard any leftover marinade.
Let the chicken rest for 3 minutes.
Warm the pita bread on the grill for about 30 seconds per side.
Assemble each pita by spreading Homemade Tzatziki, adding grilled chicken, tomatoes, cucumbers, onions, and Kalamata olives. Serve immediately.