Preheat the oven to 400°F (200°C) and line a large sheet pan with parchment paper.
Place the chicken strips, bell peppers, and red onion on the sheet pan.
Drizzle with olive oil and sprinkle with dried oregano, garlic powder, salt, and black pepper. Toss thoroughly to coat.
Arrange the chicken and vegetables in a single layer to ensure even roasting.
Roast in the center rack for 18 to 20 minutes, or until the chicken reaches an internal temperature of 165°F (74°C) and vegetables are tender.
In a small mixing bowl, whisk together the Greek yogurt, dill, chives, lemon juice, and onion powder to create the herby ranch dressing.
During the final 2 minutes of roasting, place the pitas directly on the oven rack to warm.
Slice the warm pitas in half and fill each pocket with the roasted chicken and vegetable mixture.
Drizzle the herby yogurt ranch over the filling and serve immediately.