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We determine the ability of Cosmic Explorer, a proposed third-generationgravitational-wave observatory, to detect eccentric binary neutron stars and tomeasure their eccentricity. We find that for a matched-filter search, templatebanks constructed using binaries in quasi-circular orbits are effectual foreccentric neutron star binaries with $e_{7} \leq 0.004$ ($e_{7} \leq 0.003$)for CE1 (CE2), where $e_7$ is the binary's eccentricity at a gravitational-wavefrequency of 7~Hz. We show that stochastic template placement can be used toconstruct a matched-filter search for binaries with larger eccentricities andconstruct an effectual template bank for binaries with $e_{7} \leq 0.05$. Weshow that the computational cost of both the search for binaries inquasi-circular orbits and eccentric orbits is not significantly larger forCosmic Explorer than for Advanced LIGO and is accessible with present-daycomputational resources. We investigate Cosmic Explorer's ability todistinguish between circular and eccentric binaries. We estimate that for abinary with a signal-to-noise ratio of 8 (800), Cosmic Explorer can distinguishbetween a circular binary and a binary with eccentricity $e_7 \gtrsim 10^{-2}$($10^{-3}$) at 90% confidence.

Eccentric Binary Neutron Star Search Prospects for Cosmic Explorer