Prepare the ingredients as listed.
Heat a small dry skillet over medium heat. Add the oregano, cumin, smoked paprika, garlic powder, coriander, and black pepper. Toast for 30 to 60 seconds, stirring constantly, until fragrant. Remove from the heat immediately.
Pat the chicken dry. Rub with the olive oil, lemon zest, lemon juice, salt, and half of the toasted Greek spice blend. Set aside while preparing the remaining ingredients.
Make the dill yogurt sauce by combining the Greek yogurt, fresh dill, garlic, lemon juice, and pinch of the remaining toasted spice blend. Stir well and set aside.
Place the chickpeas in a bowl and press with a fork until about half are broken open. Add the garlic, lemon juice, remaining toasted Greek spice blend, and Kalamata olives. Toss well until the chickpeas are thoroughly coated. Let stand for 5 minutes to absorb the flavors.
Heat a grill pan or grill over medium heat. Cook the chicken on both sides until to an internal temperature of 165°F (74°C). Let rest for 3 minutes, then slice into thin strips.
Warm the tortilla wraps in a dry skillet for about 20 seconds per side until soft and pliable.
Spread the hummus evenly onto the tortilla. Layer with romaine lettuce, smashed chickpeas, chicken, cucumber, tomato, red onion, and crumbled feta.
Drizzle generously with the dill yogurt sauce. Fold in the sides and roll the wraps tightly. Slice each wrap in half.
Stir together the sparkling water, lemon slices, and chia seeds. Let stand for 5 minutes, then stir again. Add ice before serving.
Serve the DD Greek Chickpea Chicken Wrap with potato chips, pickle spears, and lemon chia sparkling water.