In a bowl, stir together the olive oil, wine, lemon juice, onion, garlic, bay leaves, oregano, salt and pepper. Add the chicken pieces and turn to coat evenly. Cover and refrigerate for at least 1 hour or for up to overnight.
Prepare a medium-hot fire in a charcoal grill or preheat a cast-iron grill pan over medium-high heat. If using bamboo skewers, put 6 skewers in water to cover.
Remove the chicken pieces from the marinade and drain the bamboo skewers, if using. Thread the chicken pieces onto the bamboo or stainless-steel skewers, dividing the pieces evenly among them. Place the skewers on the grill rack 4 to 5 inches from the fire or place in the hot pan and grill, turning once, until the chicken is opaque throughout, 3 to 4 minutes per side. Season with salt and pepper.
Transfer to a warmed platter and garnish with lemon wedges and parsley. Serve immediately. Serves 6.