We have used scanning tunneling microscopy (STM) to study the initial stages of the growth of ZnSe by molecular-beam epitaxy on the GaAs(001):Se-(2X1) surface. The GaAs(001):Se-(2x1) surface is formed by depositing Se onto the GaAs(001):Se-(2X4) surface and annealing at above 520-degrees-C. It is a highly ordered (2X1) array of Se dimers, and so is structurally similar to the Se-terminated ZnSe(001)-(2X1) surface, and might be expected to provide a good starting surface for two-dimensional ZnSe growth. However, we find that ZnSe grows by the formation of three-dimensional islands on the GaAs(001):Se-(2X1) surface. Islands grow several layers high while much of the Se-terminated GaAs surface remains uncovered. We have compared our STM images to a simple statistical model of growth and conclude that the sticking coefficient of ZnSe on the GaAs(001):Se-(2X1) surface is about 1/5 of that on a continuous ZnSe film, whereas the sticking coefficient on top of the small ZnSe islands is close to that on a continuous ZnSe film. We can understand the low reactivity of the Se dimers on Ga-As compared to Se dimers on ZnSe by considering electron counting. On the ZnSe surface, Se dimers are neutral, whereas on the GaAs surface Se dimers have a net positive charge which results in a lowering of the dimer energy, producing a relatively inert surface. We conclude that in order to grow structurally high quality ZnSe films on GaAs, which requires two-dimensional growth, formation of a Se-(2X1) structure on the GaAs(001) surface must be avoided.