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Binary neutron star mergers (NSMs) have been confirmed as one source of the heaviest observable elements made by the rapid neutron-capture (r-) process. However, modeling NSM outflows—from the total ejecta masses to their elemental yields—depends on the unknown nuclear equation of state (EOS) that governs neutron star structure. In this work, we derive a phenomenological EOS by assuming that NSMs are the dominant sources of the heavy element material in metal-poor stars withr-process abundance patterns. We start with a population synthesis model to obtain a population of merging neutron star binaries and calculate their EOS-dependent elemental yields. Under the assumption that these mergers were responsible for the majority ofr-process elements in the metal-poor stars, we find parameters representing the EOS for which the theoretical NSM yields reproduce the derived abundances from observations of metal-poor stars. For our proof-of-concept assumptions, we find an EOS that is slightly softer than, but still in agreement with, current constraints, e.g., by the Neutron Star Interior Composition Explorer, withR_1.4= 12.25 ± 0.03 km andM_TOV= 2.17 ± 0.03M_⊙(statistical uncertainties, neglecting modeling systematics).