We report the discovery of the millisecond pulsar ( MSP ) PSR J1950 + 2414 ( P = 4.3 ms ) in a binary system with an eccentric ( e = 0.08 ) 22-day orbit in Pulsar ALFA survey observations with the Arecibo telescope . Its companion star has a median mass of 0.3 M _ { \odot } and is most likely a white dwarf . Fully recycled MSPs like this one are thought to be old neutron stars spun-up by mass transfer from a companion star . This process should circularize the orbit , as is observed for the vast majority of binary MSPs , which predominantly have orbital eccentricities e < 0.001 . However , four recently discovered binary MSPs have orbits with 0.027 < e < 0.44 ; PSR J1950 + 2414 is the fifth such system to be discovered . The upper limits for its intrinsic spin period derivative and inferred surface magnetic field strength are comparable to those of the general MSP population . The large eccentricities are incompatible with the predictions of the standard recycling scenario : something unusual happened during their evolution . Proposed scenarios are a ) initial evolution of the pulsar in a triple system which became dynamically unstable , b ) origin in an exchange encounter in an environment with high stellar density , c ) rotationally delayed accretion-induced collapse of a super-Chandrasekhar white dwarf , and d ) dynamical interaction of the binary with a circumbinary disk . We compare the properties of all five known eccentric MSPs with the predictions of these formation channels . Future measurements of the masses and proper motion might allow us to firmly exclude some of the proposed formation scenarios .