Into a food processor, add the garlic, oregano, smoked paprika, Kosher salt, black pepper, extra virgin olive oil, dry white wine, and lemon juice. Blend until incorporated.
Place chicken breast strips into the marinade, and allow them to marinate for 2 hours or more.
Remove the chicken breast strips from the marinade, and skewer them.
Place them into a hot grill, and cook until they are done.
Remove the skewers from the grill, remove the chicken from the skewers, and chop until 1-inch pieces.