In small bowl combine olive oil and paprika. Brush corn and chicken with oil mixture. Lightly sprinkle salt and pepper. Grill directly over medium coals for 12 to 15 minutes or until chicken is no longer pink (170 degrees F), turning once.
Carefully cut kernels from cob by firmly holding the corn at the top (using a kitchen towel to grip, if necessary) and slicing downward with a sharp knife. Transfer to bowl; stir in sour cream. Season with additional salt and pepper. Stir in milk to desired creaminess. Slice chicken breasts. Serve with corn; sprinkle shredded basil. Serves 4.