We define a new solution concept for transferable utility cooperative games in characteristic function form, in a framework where individuals believe in equality as a desirable social goal, although private preferences dictate selfish behavior. This latter aspect implies that the solution outcome(s) must satisfy core-like participation constraints while the concern for equality entails choice of Lorenz maximal elements from within the set of payoffs satisfying the participation constraints. Despite the Lorenz domination relation being a partial ranking, we show that the egalitarian solution is unique whenever it exists. Moreover, for convex games, the solution is in the core and Lorenz dominates every other core allocation.