While the last century brought an exquisite understanding of the molecular basis of life, very little is known about the detailed chemical mechanisms that afforded the emergence of life on early earth. There is a broad agreement that the problem lies in the realm of chemistry, and likely resides in the formation and mutual interactions of carbon-based molecules in aqueous medium. Yet, present-day experimental approaches can only capture the synthesis and behavior of a few molecule types at a time. On the other hand, experimental simulations of prebiotic syntheses, as well as chemical analyses of carbonaceous meteorites, suggest that the early prebiotic hydrosphere contained many thousands of different compounds. The present paper explores the idea that given the limitations of test-tube approaches with regards to such a `random chemistry’ scenario, an alternative mode of analysis should be pursued. It is argued that as computational tools for the reconstruction of molecular interactions improve rapidly, it may soon become possible to perform adequate computer-based simulations of prebiotic evolution. We thus propose to launch a computational origin of life endeavor (http://ool.weizmann.ac.il/CORE), involving computer simulations of realistic complex prebiotic chemical networks. In the present paper we provide specific examples, based on a novel algorithmic approach, which constitutes a hybrid of molecular dynamics and stochastic chemistry. As one potential solution for the immense hardware requirements dictated by this approach, we have begun to implement an idle CPU harvesting scheme, under the title ool@home.