The Alfred Hitchcock Hour - Season 1 Episode 30 : Dear Uncle George 1965

John Chambers writes an advice to the lovelorn column under the pseudonymn Uncle George. He learns that his wife is cheating on him when a neighbor named Mrs. Weatherby, not knowing that John and Uncle George are the same person, writes a letter to his column asking for advice. Chambers kills his wife and then pins the blame on her lover. When he fakes shock when the police reveal his wife's affair, he is accepted as innocent because he doesn't have a motive. Chambers almost gets away with murder until Mrs. Weatherby tells the police that she mailed the Uncle George column asking for advice about the situation.