"An Unearthly Child" was the first televised story of Doctor Who. It premiered on Saturday, 23rd November, 1963 at 5:15pm.
As this was the day immediately after the assassination of President Kennedy, the BBC, worried that not many people had seen the episode, decided to show it again the following Saturday, along with the second episode.
A trailer starring William Hartnell in character had been shown a week before, although it no longer exists in the archives. A fan-made reconstruction can be seen here though.
See also this piece from the BBC archives which includes a snapshot of the page in Radio Times showing the episode's original listing in the schedule.