Preheat your grill or grill pan to medium-high heat.
In a small bowl, whisk together the minced garlic, dried oregano, thyme, rosemary, lemon juice, olive oil, salt, and pepper to make the marinade.
Place the chicken breasts in a shallow dish or resealable plastic bag, and pour the marinade over them, ensuring they are well coated.
Marinate the chicken in the refrigerator for at least 30 minutes, or up to 4 hours.
While the chicken is marinating, prepare the other ingredients for the pita pockets.
Dice the cucumber and tomato, slice the red onion, crumble the feta cheese, and set aside.
Grill the marinated chicken breasts for about 6-8 minutes per side, or until they are cooked through and have nice grill marks.
Remove from the grill and let them rest for a few minutes before slicing into thin strips.
Warm the pita bread rounds on the grill or in the oven according to package instructions.
To assemble the pita pockets, open each warmed pita bread round and fill it with sliced grilled chicken, diced cucumber, diced tomato, sliced red onion, crumbled feta cheese, and a dollop of tzatziki sauce.
You can add optional toppings such as sliced black olives, chopped fresh parsley, or sliced bell peppers.
Serve the Greek Chicken Pita Pockets with a side salad or with hummus!