Amman, Jordan, “Black September” 1970: the Jordanians are determined to dislodge the PLO from its city-center strongholds. Among the journalists caught in the crossfire is Sullivan (Bill Paterson). Sympathetic to the PLO cause, he is asked to identify a woman (Tilda Swinton) picked up without passport or papers. Sullivan pretends to know her, and takes her to his hotel, where she discloses that she is an extra-terrestrial, code-named Friendship, and sent from the galaxy of Procryon to make contact with advanced members of the human species. Due to a malfunction during atmospheric entry, she lost contact with her base, and landed in Amman, instead of at the Massachusetts Institute of Technology.

After some hesitation, Sullivan decides to accept her story, alternately plying her with alcohol and pumping her for information, intrigued by his feelings for a creature who is a perfect simulation of a white Anglo-Saxon woman. Friendship, meanwhile, less and less interested in her mission, becomes absorbed in the street life of Amman and the moral paradoxes arising from an incident at the historic ruins of Jedash, where her Palestinian guide is taken hostage by the Jordanian army.

Sullivan uses her absence to search her room, where he takes a handful of colored crystals, which that night begin to glow and emit sounds. Friendship, alerted by him, explains that the crystals are electronic note-pads, and lets him keep one as a memento. The following day, the house-to-house fighting has reached the hotel, and Sullivan is able to obtain two passes for Damascus. But Friendship refuses to go: as a robot without a home or a recognized history, her closest kin are the dispossessed Palestinians, whose fate – whatever it might be – she wants to share.

It is in fact a meeting years later back in London with his friend Kubler from the International Red Cross (Patrick Bauchau) that has reminded Sullivan of Friendship, whose death during the September massacres he assumes as certain. His teenage daughter, a computer wizard, asks for the crystal and is allowed to test it with some new equipment. One day, she plays it to her father as a videotape: body-scan images, shots of Amman, strange colors and shapes come together in Friendship's accidental testament: a message without a code, from a sender without an addressee.