Clean chicken by running it under cold water, pat dry with paper towels. Cut and discard any fat pieces.
Cut chicken into 3 inch cubes and add to a large ziplock bag.
In a medium bowl mix the rest of the ingredients: olive oil, buttermilk, Italian seasoning, parsley, garlic, lemon juice, lemon zest, salt and pepper. Whisk until fully combined. Pour the mixture on top of the chicken.
Close the ziplock bag, shake to coat the chicken evenly in the marinade and refrigerate for at least one hour or overnight. Preferably, shake and toss the chicken during this period a few times, so it marinates evenly.
For outdoor grilling, heat the grill until hot and spray it with cooking oil. For indoor cooking, place a cast iron grill pan oven medium-high heat and add to it about 2 tablespoons of olive oil.
If desired, arrange the chicken pieces on wooden skewers. Grill for 3-4 minutes on each side, or until the chicken is no longer pink in the middle.
Serve with a salad, lemon and your favorite dressing for dipping.