The challenge of prebiotic chemistry is to trace the syntheses of life's key building blocks from a handful of primordial substrates. Here we report a forward-synthesis algorithm that generates a full network of prebiotic chemical reactions accessible from these substrates under generally accepted conditions. This network contains both reported and previously unidentified routes to biotic targets, as well as plausible syntheses of abiotic molecules. It also exhibits three forms of nontrivial chemical emergence, as the molecules within the network can act as catalysts of downstream reaction types; form functional chemical systems, including self-regenerating cycles; and produce surfactants relevant to primitive forms of biological compartmentalization. To support these claims, computer-predicted, prebiotic syntheses of several biotic molecules as well as a multistep, self-regenerative cycle of iminodiacetic acid were validated by experiment.