In a bowl, combine olive oil, lemon juice, garlic, oregano, salt, and black pepper. Add the chicken breasts and coat well. Marinate for at least 30 minutes.

Preheat the grill to medium-high heat. Remove the chicken from the marinade and grill for 6-7 minutes per side, or until the internal temperature reaches 165°F (75°C).

Toast the bread or buns on the grill for 1-2 minutes. Layer lettuce, grilled chicken, tomato, cheese, and mayonnaise on the bread. Top with another slice of bread or bun.

Cut the sandwich in half and serve immediately with your choice of sides.