Add the wine, oil, lemon juice, salt, pepper, Italian seasoning, garlic and paprika to a shallow baking dish or container and whisk well to combine.
Add the chicken legs (trim any excess fat first) skin-side down and spoon some marinade over them. Cover, and refrigerate for 20 minutes to 2 hours.
Preheat your grill to medium-high and once the grill is hot, add the chicken legs skin-side down.
Grill for about 11 minutes per side, or until they've reached a golden brown with grill marks. Test the internal temperature to be sure it's 74 degrees Celsius (165 Fahrenheit) before removing from the grill.
Let the chicken rest for about 5 minutes before enjoying (cover loosely with foil while resting).