In a large mixing bowl, combine the olive oil, minced garlic, oregano, basil, salt, pepper, and lemon juice. Whisk together until well mixed.
Add the cubed chicken to the marinade, ensuring each piece is well coated. Cover the bowl with plastic wrap and let it marinate in the refrigerator for at least 30 minutes, or up to 2 hours for more flavor.
Preheat your grill or grill pan over medium-high heat.
Thread the marinated chicken onto the skewers, leaving a little space between each piece for even cooking.
Once the grill is hot, place the skewers on the grill. Cook for about 5 minutes, then turn the skewers and cook for an additional 5 minutes, or until the chicken is cooked through and has nice grill marks.
During the last couple of minutes of grilling, sprinkle the grated Parmesan cheese over the skewers and close the grill lid, allowing the cheese to melt slightly.
Remove the skewers from the grill and allow them to rest for a couple of minutes. Garnish with chopped fresh parsley if desired before serving.