Why are vain people said to be “looking for the limelight”?

In the early days of theatre, the players were lit by gas lamps hidden across the front of the stage. Early in the twentieth century, it was discovered that if a stick of lime was added to the gas, the light became more intense, and so they began to use the “limelight” to illuminate the spot on stage where the most important part of the play took place. Later called the “spotlight,” the “limelight” was where all actors fought to be.