Cut the chicken breasts into approximately 1 1/2-inch cubes, keeping the pieces similar in size for even cooking.
Add the chicken to a large mixing bowl. Pour in the olive oil and lemon juice, then add the minced garlic, oregano, parsley, salt, and black pepper.
Toss thoroughly until every piece of chicken is coated in the marinade.
Cover the bowl and refrigerate for at least 30 minutes to allow the flavors to develop.
Preheat an outdoor grill or grill pan to medium-high heat.
Thread the marinated chicken pieces onto skewers, leaving just a little space between the pieces so they cook evenly.
Place the Greek Chicken Souvlaki skewers on the hot grill and cook for approximately 3–4 minutes on each side, turning as needed.
Continue grilling until the outside is lightly charred and the chicken reaches a safe internal temperature of 165°F (74°C).
Transfer the skewers to a clean platter and let them rest for a few minutes.
Serve warm with tzatziki sauce and your favorite Mediterranean-inspired sides.