Apparently composer John Berry's first choice to sing his iconic theme song was Anthony Newley. The story goes that Berry used this recording of Newley to demo the song.
It seems that I had the story about this song wrong. In fact Anthony Newley co-wrote the lyrics and his recording of it was in fact a way to demo the completed song. It appears this version was never under consideration for the movie.
I couldn't find a version that was synced up with the movie's opening titles.
Previous Rejected Bond Themes.
"For Your Eyes Only" by Blondie
"Quantum of Solace" by Shirley Bassey
"Thunderball" by Johnny Cash
The video I posted earlier of "The Man With The Golden Gun" by Alice Cooper has now been taken down.