With strongly bound and stable excitons at room temperature, single-layer, two-dimensional organic-inorganic hybrid perovskites are viable semiconductors for light-emitting quantum optoelectronics applications. In such a technological context, it is imperative to comprehensively explore all the factors --- chemical, electronic and structural --- that govern strong multi-exciton correlations. Here, by means of two-dimensional coherent spectroscopy, we examine excitonic many-body effects in pure,

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... single-layer (PEA)_2PbI_4 (PEA = phenylethylammonium). We determine the binding energy of biexcitons --- correlated two-electron, two-hole quasiparticles --- to be 44 ± 5 meV at room temperature. The extraordinarily high values are similar to those reported in other strongly excitonic two-dimensional materials such as transition-metal dichalchogenides. Importantly, we show that this binding energy increases by ∼25% upon cooling to 5 K. Our work highlights the importance of multi-exciton correlations in this class of technologically promising, solution-processable materials, in spite of the strong effects of lattice fluctuations and dynamic disorder.