Despite the popularity of equality as a political value, egalitarianism as a political theory has never, I think, been fully or successfully defended. I aim in this paper to begin the defense of such a view. The egalitarianism I have in mind has as its ideal a condition of equal wellbeing for all persons at the highest possible level of well-being, i.e. maximum equal well-being. Egalitarianism holds that society should be arranged so as to promote and maintain this state. Defending such a view involves, as I see it, three tasks. First, the ideal I have Just mentioned must be made clearer and more specific and its implications for the distribution of particular goods such as material possessions and liberty must be revealed. Second, positive arguments must be given in support of an equal distribution of well-being as a requirement of morality and Justice. And, thirdly, arguments to the effect that there are Just or Justified inequalities which seriously outweigh the claims of equality must be rebutted.