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By nature of their small size, dense growth and frequent need for extracellular metabolism, microbes face persistent public goods dilemmas. Genetic assortment is the only general solution stabilizing cooperation, but all known mechanisms structuring microbial populations depend on the availability of free space, an often unrealistic constraint. Here we describe a class of self-organization that operates within densely packed bacterial populations. Through mathematical modelling and experiments with Vibrio cholerae, we show how killing adjacent competitors via the Type VI secretion system (T6SS) precipitates phase separation via the 'Model A' universality class of order-disorder transition mediated by killing. We mathematically demonstrate that T6SS-mediated killing should favour the evolution of public goods cooperation, and empirically support this prediction using a phylogenetic comparative analysis. This work illustrates the twin role played by the T6SS, dealing death to local competitors while simultaneously creating conditions potentially favouring the evolution of cooperation with kin.