In a bowl, mix Greek yogurt, garlic, lemon juice, oregano, salt, and pepper. Add chicken breasts and coat well. Marinate for at least 1 hour or overnight.

Preheat grill or skillet over medium-high heat. Cook marinated chicken for 6-7 minutes on each side until golden brown and internal temperature reaches 165°F (75°C). Let rest before slicing.

Grate cucumber and remove excess moisture. Mix with Greek yogurt, garlic, lemon juice, salt, and chopped dill if desired to make tzatziki sauce.

Warm pita on the grill or dry skillet until soft.

Slice chicken and layer on warmed pita with tzatziki and optional toppings like lettuce or tomatoes.