When the Walk of Fame first started, they immediately installed a huge number of stars (over 1,500) honoring past & present Hollywood greats. So there really was no "first" star.
However, they then began adding new stars one at a time after that, and have been doing so for 50 years. The first person to get a star AFTER that first mass installation was actress Joanne Woodward (Mrs. Paul Newman).
The first star placed on the Hollywood Walk of Fame on February 9, 1960, was for Joanne Woodward.
If you want more facts go to this website http://uk.ask.com/wiki/Hollywood_Walk_of_Fame.