The Eridanus II (EriII) 'ultra-faint' dwarf has a large (15 pc) and low mass (4.3 × 10 3 M ) star cluster (SC) offset from its centre by 23 ± 3 pc in projection. Its size and offset are naturally explained if EriII has a central dark matter core, but such a core may be challenging to explain in a ΛCDM cosmology. In this paper, we revisit the survival and evolution of EriII's SC, focussing for the first time on its puzzingly large ellipticity (0.31 +0.05 −0.06 ). We perform a suite of 960 direct 𝑁-body simulations of SCs, orbiting within a range of spherical background potentials fit to ultra-faint dwarf galaxy simulations. We find only two scenarios that come close to explaining EriII's SC. In the first, EriII has a low density dark matter core (of size ∼ 70 pc and density 2 × 10 8 M kpc −3 ). In this model, the high ellipticity of EriII's SC is set at birth, with the lack of tidal forces in the core allowing its ellipticity to remain frozen in for long times. In the second, EriII's SC orbits in a partial core, with its high ellipticity owing to its imminent tidal destruction. However, this latter model predicts more substantial tidal tails around EriII's SC that should have already been seen in the data, leading us to favour the cored model. We discuss potential caveats to these findings, and the implications of the cored model for galaxy formation and the nature of dark matter.