We have discovered a highly eccentric (e = 0.95) binary millisecond pulsar (MSP) in the globular cluster NGC 6652, a cluster that previously contained no known MSPs. We targeted the cluster with the GBT following its detection at gamma-ray energies by the Fermi Large Area Telescope (LAT), under the hypothesis that the high-energy emission originates from a population of MSPs in the cluster. An initial timing solution shows that the MSP is in a very eccentric orbit, and that its companion's minimum mass is 0.73 solar masses. The high eccentricity and unusually large companion mass together indicate that this system underwent a companion exchange after the MSP completed its accretion and spin-up (recycling) evolutionary stage. The very high eccentricity of this system will allow us to measure the orbital precession rate after a few months to a year of timing, yielding the total system mass and constraining the mass of the neutron star. Measurements of one or more other post-Keplerian parameters are likely, and will allow us to measure the neutron star mass and potentially to test general relativity.