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The LIGO/Virgo collaborations recently announced the detection of a likely binary neutron star merger, GW190425. The total mass of GW190425 is significantly larger than the masses of Galactic double neutron stars known through radio astronomy. This suggests that GW190425 formed differently from Galactic double neutron stars. We hypothesize that GW190425 formed via unstable "case BB" mass transfer. According to this hypothesis, the progenitor of GW190425 was a binary consisting of a neutron star and a ${\sim} 4-5 {M_\odot}$ helium star, which underwent a common-envelope process. Following the supernovae of the helium star core, a tight, eccentric, double neutron star was formed, which merged in ${\lesssim}$ 10 Myr. The helium star progenitor may explain the unusually large mass of GW190425, while the short time to merger may explain why we do not see similar systems in radio. In order to test this hypothesis, we measure the eccentricity of GW190425 using publicly available LIGO/Virgo data. We constrain the eccentricity at 10 Hz to be $e \leq 0.007$ with $90\%$ confidence. This result provides no evidence for or against the unstable mass transfer scenario because the binary is likely to have circularized to $e\lesssim10^{-4}$ by the time it entered the LIGO/Virgo band. Future detectors operating in lower frequency bands will enable us to discern the formation channel of mergers similar to GW190425 using eccentricity measurements.