A 1964 interview of Ayn Rand from Playboy magazine.
Galt's statement is a dramatized summation of the Objectivist ethics. Any system of ethics is based on and derived, implicitly or explicitly, from a metaphysics. The ethic derived from the metaphysical base of Objectivism holds that, since reason is man's basic tool of survival, rationality is his highest virtue. To use his mind, to perceive reality and to act accordingly, is man's moral imperative. The standard of value of the Objectivist ethics is: man's life -- man's survival qua man -- or that which the nature of a rational being requires for his proper survival. The Objectivist ethics, in essence, hold that man exists for his own sake, that the pursuit of his own happiness is his highest moral purpose, that he must not sacrifice himself to others, nor sacrifice others to himself. It is this last that Galt's statement summarizes.
Rand is nothing if not decisive and consistent in her answers...except where she contradicts herself. (Aside: I would love to read a blog written by Fake Ayn Rand where she reviews current movies. Someone start that up, please.)