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We report on photoluminescence in the 3-7 $\mu$m mid-wave infrared (MWIR) range from sub-100 nm strained thin films of rocksalt PbSe(001) grown on GaAs(001) substrates by molecular beam epitaxy. These bare films, grown epitaxially at temperatures below 400 {\deg}C, luminesce brightly at room temperature and have minority carrier lifetimes as long as 172 ns. The relatively long lifetimes in PbSe thin films are achievable despite threading dislocation densities exceeding $10^9$ $cm^{-2}$ arising from island growth on the nearly 8% lattice- and crystal-structure-mismatched GaAs substrate. Using quasi-continuous-wave and time-resolved photoluminescence, we show Shockley-Read-Hall recombination is slow in our high dislocation density PbSe films at room temperature, a hallmark of defect tolerance. Power-dependent photoluminescence and high injection excess carrier lifetimes at room temperature suggest that degenerate Auger recombination limits the efficiency of our films, though the Auger recombination rates are significantly lower than equivalent, III-V bulk materials and even a bit slower than expectations for bulk PbSe. Consequently, the combined effects of defect tolerance and low Auger recombination rates yield an estimated peak internal quantum efficiency of roughly 30% at room temperature, unparalleled in the MWIR for a severely lattice-mismatched thin film. We anticipate substantial opportunities for improving performance by optimizing crystal growth as well as understanding Auger processes in thin films. These results highlight the unique opportunity to harness the unusual chemical bonding in PbSe and related IV-VI semiconductors for heterogeneously integrated mid-infrared light sources constrained by tight thermal budgets in new device designs., Comment: 24 pages, 6 figures