We present the Robert C. Byrd Green Bank Telescope discovery of the highly eccentric binary millisecond pulsar PSR J1835 - 3259A in the Fermi Large Area Telescope-detected globular cluster NGC 6652 . Timing over one orbit yields the pulse period 3.89 ms , orbital period 9.25 d , eccentricity \sim 0.95 , and an unusually high companion mass of 0.74 M _ { \odot } assuming a 1.4 M _ { \odot } pulsar . We caution that the lack of data near periastron prevents a precise measurement of the eccentricity , and that further timing is necessary to constrain this and the other orbital parameters . From tidal considerations , we find that the companion must be a compact object . This system likely formed through an exchange encounter in the dense cluster environment . Our initial timing results predict the measurements of at least two post-Keplerian parameters with long-term phase-connected timing : the rate of periastron advance \dot { \omega } \sim 0.1 \arcdeg yr ^ { -1 } , requiring 1 yr of phase connection ; and the Einstein delay \gamma _ { \mathrm { GR } } \sim 10 ms , requiring 2–3 yr of timing . For an orbital inclination i > 50 ^ { \circ } , a measurement of \sin { i } is also likely . PSR J1835 - 3259A thus provides an opportunity to measure the neutron star mass with high precision ; to probe the cluster environment ; and , depending on the nature of the companion , to investigate the limits of general relativity .