Marinate the chicken: In a large bowl, add the chicken, yogurt, olive oil, lemon zest and juice, garlic, dill, salt, pepper, paprika and oregano. Stir until the chicken is well coated with the yogurt and spices. Cover and set aside for at last 20 minutes while you chop your vegetables and prepare your sauce.
Make the sauce: In a medium bowl, stir the yogurt, cucumber, dill and parsley, garlic, lemon juice and salt until well combined. Place in the fridge until ready to serve. This can be made a day in advance, if desired.
Preheat your grill to medium-high heat, about 400 degrees F. Scrape off any leftover bits from the last time you grilled.
Prepare vegetables: Drizzle the vegetables with olive oil and season with salt and pepper. Use clean hands to toss veggies with oil so that they are well coated.
Cook the chicken and vegetables: Add the chicken in a single layer on one side of the grill and the vegetables in a single layer on the other side, placing at least an inch apart. Grill with the lid closed, until a meat thermometer inserted into the center reads 165 degrees F, flipping halfway through, about 6 to 8 minutes per side. The vegetables will grill for about the same amount of time. Transfer the chicken and vegetable to a platter and allow the chicken to rest for a few minutes to retain the juiciness of the chicken.
Warm the pita: Turn off the grill and immediately add the pita to the grill. Close and warm for 2 minutes per side.
Chop the chicken and veggies: Give the vegetables a rough chop so that they are all roughly the same size. Next, chop or slice the chicken into pieces.
Serve: Add a scoop of the herb cucumber yogurt sauce to a shallow bowl, then add some of each veggie, the chicken, and roasted chickpeas, if using. Top with pickled red onion and serve with warm toasted pita. Garnish with extra dill and parsley and dig in!