In a bowl, combine the chopped basil, lemon juice, olive oil, minced garlic, dried oregano, sea salt, and dried rosemary (if using). Mix well.
Add the bite-sized chicken pieces to the marinade. Toss to coat the chicken evenly. Cover the bowl and let it marinate in the refrigerator for at least 1 hour, or up to 4 hours for better flavor and tenderness.
If using wooden skewers, soak them in water for at least 30 minutes to prevent burning. Thread the marinated chicken pieces onto the skewers, leaving a little space between each piece.
Preheat the grill to medium-high heat. Place the skewers on the grill and cook for about 10-12 minutes, turning occasionally, until the chicken is cooked through and has a nice char. The internal temperature of the chicken should reach 165°F (74°C).
Remove the skewers from the grill and let them rest for a few minutes before serving. Garnish with additional chopped basil if desired.