Combine the smoked paprika, salt, cumin, garlic powder, basil (or Italian seasoning), black pepper, cayenne pepper, and olive oil in a gallon sized ziploc bag. Knead to combine ingredients.
Add in the chicken and knead to coat. Place in the fridge for up to 8 hours.
Preheat an outdoor grill to medium or medium-high. (Alternately, you could cook the chicken in a skillet on the stove or broil in the oven.) Grill for 4-6 minutes per side until cooked through. Serves 4-6.