In a large bowl, combine the chicken thighs, Greek yogurt, olive oil, lemon zest, lemon juice, garlic, dill, salt, pepper, paprika, and oregano. Mix until the chicken is thoroughly coated. Cover and marinate for at least 20 minutes.
Prepare the tzatziki sauce by mixing the Greek yogurt, shredded cucumber, dill, parsley, garlic, lemon juice, and salt in a medium bowl. Refrigerate until serving.
Preheat the grill to medium-high heat, approximately 400°F (200°C).
Place the vegetables in a large bowl. Drizzle with olive oil and season with salt and pepper. Toss until evenly coated.
Arrange the chicken on one side of the grill and the vegetables on the other side in a single layer.
Grill the chicken for 6–8 minutes per side, flipping once, until it reaches an internal temperature of 165°F (74°C).
Grill the vegetables for approximately the same amount of time, turning as needed until tender and lightly charred.
Transfer everything to a serving platter and allow the chicken to rest for several minutes. This helps retain its juices.
Warm the pita bread on the grill for about 2 minutes per side.
Roughly chop the vegetables and slice the chicken into bite-sized pieces.
To serve this Grilled Mediterranean Chicken and Vegetables recipe, spread a spoonful of tzatziki into a shallow bowl or serving platter. Add the grilled chicken, vegetables, roasted chickpeas, and pita. Garnish with pickled red onion, dill, and parsley.