Season the chicken breasts with olive oil, salt, pepper, and dried oregano. Grill them on medium-high heat for about 6-7 minutes on each side or until fully cooked. Let them rest before slicing.
In a bowl, combine the Greek yogurt, lemon juice, minced garlic, diced cucumber, salt, and pepper. Mix well and refrigerate for at least 15 minutes to allow the flavors to meld.
Warm the pita pockets in a dry skillet over medium heat for 1-2 minutes on each side until soft and pliable.
Slice the warm pita pockets open to create a pocket. Start by adding a layer of shredded romaine lettuce, followed by the grilled chicken slices, diced tomatoes, and red onions.
Generously drizzle the tzatziki sauce over the fillings in each pita pocket.
Serve immediately while warm, or pack for lunch on-the-go!