Preheat the oven to 425°F (220°C).
Place the sliced bell peppers on a sheet pan. Drizzle lightly with olive oil, season with salt, and toss.
Roast the peppers for 10 minutes.
Meanwhile, combine the chicken with garlic, olive oil, lemon juice, cumin, smoked paprika, salt, curry powder, and black pepper.
Remove the sheet pan from the oven and arrange the chicken beside the peppers.
Return the pan to the oven and cook for another 10–12 minutes, until the chicken reaches 165°F (74°C) internally.
To make the tzatziki, squeeze excess moisture from the grated cucumber.
Mix the cucumber with Greek yogurt, lemon juice, olive oil, garlic, dill, salt, and pepper.
Dice the fresh cucumber and red onion and prepare the olives, feta, and pita bread.
Warm the pita breads briefly.
Fill or top each pita with chicken, roasted peppers, cucumber, red onion, olives, and feta.
Finish with a generous spoonful of tzatziki and serve immediately.