In a non-reactive bowl, whisk together olive oil, lemon juice, minced garlic, oregano, salt, and pepper to create the marinade.
Place chicken cubes into a resealable plastic bag or glass dish and coat thoroughly with the marinade; refrigerate for at least 1 hour.
Thread the marinated chicken pieces onto the soaked skewers, leaving minimal space between pieces to retain moisture.
Preheat an outdoor grill or indoor grill pan to medium-high heat (approximately 400°F).
Place skewers on the grill grate and cook for 10 to 12 minutes, turning every 3 to 4 minutes to ensure even browning and internal doneness.
Verify chicken has reached an internal temperature of 165°F (74°C) using an instant-read thermometer.
Transfer skewers to a platter and allow the meat to rest for 3 minutes before service.