In a bowl, combine the soy sauce, honey, mirin, rice vinegar, minced garlic, and grated ginger. Subsequently, mix well to create the teriyaki marinade.
Place the chicken pieces in a zip-top bag and pour the marinade over them. Close the bag and gently massage it until you evenly coat the chicken. Allow the chicken to marinate in the fridge for at least 30 minutes, or up to 24 hours for maximum flavor.
Preheat your grill to medium-high heat. Additionally, if you use a charcoal grill, ensure you have evenly lit coals and clean grill grates.
Thread the marinated chicken pieces onto the soaked wooden skewers, leaving a little space between each piece.
Brush vegetable oil on the grill to prevent sticking. Cook for 4-5 minutes per side, or until the chicken is cooked through and slightly charred.
While the chicken is grilling, you can brush some of the remaining marinade on the skewers for an extra burst of flavor.
Once you've cooked the chicken, remove the skewers from the grill and let them rest for a few minutes before serving.
Serve the teriyaki chicken skewers hot, either as a main dish with steamed rice and vegetables, or as an appetizer at your next gathering.