In axiomatic bargaining (choice theory), a choice function of some importance is the utilitarian choice function. Basically, this choice function selects the vector of utilities whose sum is greatest, among all utility vectors. There have been several axiomatic characterizations of the utilitarian choice function. Notable among them are the ones due to Myerson (1981), and Moulin (1988). A variant of the utilitarian choice function, called the additive choice function (: the latter being defined on a larger domain, than the domain permissible for the utilitarian choice function) has been axiomatically characterized in Lahiri (forthcoming). In this paper, we present an axiomatic characterization of the utilitarian choice function, which is similar to the axiomatic characterization in Moulin [1988], except that we now replace Nash's Independence of Irrelevant Alternatives by an assumption called Weak Localization, essentially due to Peters [1992].