Elaan of Troyius

"Elaan of Troyius" is a third-season episode of the original science fiction television series Star Trek, and was broadcast December 20, 1968. It is episode #68, production #57, and was written and directed by John Meredyth Lucas, the only person ever in Star Trek production history to both write and direct a filmed Star Trek television episode, whether animated or live-action.
In this episode, the USS Enterprise ferries a spoiled princess whose betrothal to a royal Troyian is hoped will bring peace to a star system at war.
Plot
On stardate 4372.5, the Federation starship USS Enterprise arrives at the planet Troyius, the outermost world in the Tellun System, to pick up Petri, a green-skinned, white-haired Troyian ambassador. He is then taken to Elas, the innermost planet to pick up the Dohlman, Elaan – a beautiful but very demanding young woman who is a member of a royal family. Though she is politically powerful...