Many eukaryotic cells, including Dictyostelium discoideum amoebae, fibroblasts, and neutrophils, are able to respond to chemoattractant gradients with high sensitivity. Recent studies have demonstrated that, after the introduction of a chemoattractant gradient, several chemotaxis pathway components exhibit a subcellular reorganization that cannot be described as a simple amplification of the external gradient. Instead, this reorganization has the characteristics of a switch, leading to a well defined front and back. Here, we propose a directional sensing mechanism in which two second messengers are produced at equal rates. The diffusion of one of them, coupled with an inactivation scheme, ensures a switch-like response to external gradients for a large range of gradient steepness and average concentration. Furthermore, our model is able to reverse the subcellular organization rapidly, and its response to multiple simultaneous chemoattractant sources is in good agreement with recent experimental results. Finally, we propose that the dynamics of a heterotrimeric G protein might allow for a specific biochemical realization of our model.