The emergence of new banking technologies will profoundly influence the nature of financial intermediation, the structure of banking markets and the form of competition between banks. This paper analyses a model of a stochastic oligopoly, in which the form of competition between rival banks is the endogenous outcome of a choice between alternative strategies regarding the timing of investment in an electronic banking technology, relative to the resolution of uncertainty over the demand for electronic banking services. The opportunity to invest in such technology is a real option held by each bank. Each bank must decide on the timing of the exercise of its option when the payoff to the exercise of the option will depend on both realized demand for banking services and on the exercise strategy adopted by its rivals. The sequential equilibrium in this game is a generalized Cournot solution, in which each bank adopts a mixed strategy regarding the timing of the exercise of its investment option and in which the probability of early exercise is decreasing in the degree of demand uncertainty.