Remarkably it was recently bought for just £25 at a car boot sale.
During the the 1965 movie, 007's mission is to find two NATO atomic bombs stolen by SPECTRE.
The 1962 watch, modified by the James Bond art department to include a 'Geiger counter' (one of the hands of the watch shows the strength of radioactivity), was the only one produced for the movie.
Its whereabouts has long been a mystery, although it is thought to been given to a member of the crew at Pinewood Studios, where much of the movie was made.
The estimate is £40,000-60,000.
Tel: 020 7930 6074.