Cut the chicken into 2-inch cubes.
Make the spiedie marinade: In a large non-reactive bowl, combine the oil, vinegar, lemon juice, garlic, parsley, oregano, salt, and pepper.
Add the chicken and stir to coat well. Cover and refrigerate at least 3 hours, or up to 2 days.
Thread the chicken onto skewers; discard any remaining marinade.
Grill the chicken over high heat for 10-15 minutes, or until cooked through. Alternatively, cook the chicken in a cast iron skillet over medium-high heat for 8-12 minutes, or until cooked.
Serve the spiedie chicken on a roll with lemon wedges.