In a large mixing bowl, combine Greek yogurt, olive oil, lemon juice, minced garlic, kosher salt, black pepper, dried oregano, and paprika. Stir until well mixed. Add in the chicken thighs or breasts, ensuring each piece is thoroughly coated with the marinade. Cover the bowl and refrigerate for a minimum of 2 hours, but ideally overnight for maximum flavor.

Heat a large skillet over medium-high heat and add a drizzle of olive oil. Once hot, carefully place the marinated chicken in the pan, cooking for 3-4 minutes on each side until golden brown and cooked through, reaching an internal temperature of 165°F. Alternatively, grill the chicken for about 2-3 minutes per side.

While the chicken is cooking, prepare the tzatziki sauce by grating the cucumbers and squeezing out excess moisture. In a mixing bowl, combine the grated cucumbers with fresh dill, Greek yogurt, lemon juice, minced garlic, olive oil, kosher salt, and black pepper. Stir until blended.

To warm the pita bread, heat a grill, stovetop, or toaster oven. Lightly grill or toast the pita for about 1-2 minutes on each side until soft and slightly golden.

To assemble your Greek Chicken Gyros, spread a layer of tzatziki sauce across the warmed pita. Add sliced, cooked chicken, and top with fresh vegetables like lettuce, diced tomatoes, cucumbers, and red onion. Wrap the pita around the fillings and serve immediately.