This is the story that coined the phrase "Mary Sue". It appeared in 1974, in the zine "the Menagerie".
A TREKKIE'S TALE
By Paula Smith
"Gee, golly, gosh, gloriosky," thought Mary Sue as she stepped on the bridge of the Enterprise. "Here I am, the youngest lieutenant in the fleet - only fifteen and a half years old." Captain Kirk came up to her.
"Oh, Lieutenant, I love you madly. Will you come to bed with me?"
"Captain! I am not that kind of girl!"
"You're right, and I respect you for it. Here, take over the ship for a minute while I go get some coffee for us."
Mr. Spock came onto the bridge. "What are you doing in the command seat, Lieutenant?"
"The Captain told me to."
"Flawlessly logical. I admire your mind."
Captain Kirk, Mr. Spock, Dr. McCoy and Mr. Scott beamed down with Lt. Mary Sue to Rigel XXXVII. They were attacked by green androids and thrown into prison. In a moment of weakness Lt. Mary Sue revealed to Mr. Spock that she too was half Vulcan. Recovering quickly, she sprung the lock with her hairpin and they all got away back to the ship.
But back on board, Dr. McCoy and Lt. Mary Sue found out that the men who had beamed down were seriously stricken by the jumping cold robbies , Mary Sue less so. While the four officers languished in Sick Bay, Lt. Mary Sue ran the ship, and ran it so well she received the Nobel Peace Prize, the Vulcan Order of Gallantry and the Tralfamadorian Order of Good Guyhood.
However the disease finally got to her and she fell fatally ill. In the Sick Bay as she breathed her last, she was surrounded by Captain Kirk, Mr. Spock, Dr. McCoy, and Mr. Scott, all weeping unashamedly at the loss of her beautiful youth and youthful beauty, intelligence, capability and all around niceness. Even to this day her birthday is a national holiday of the Enterprise.