USS Unicorn (SS-429), a Balao-class submarine, was the first submarine of the United States Navy to be given that name for the narwhal, an Arctic marine cetacean with a single tusk suggesting the horn of a unicorn and therefore sometimes called the "sea unicorn." She was never built.
The contract for Unicorn's construction was authorized on 9 July 1942 and her keel was scheduled to be laid down by the Cramp Shipbuilding Company of Philadelphia, Pennsylvania, but she was cancelled on 29 July 1944 before construction could begin.