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The binary millisecond pulsar J1713+0747 $({\rm P}=4.57~{\rm ms};{\rm P_b}=67.8~{\rm d})$ was discovered in a systematic continuing survey for millisecond pulsars with the Arecibo radio telescope (Foster, Wolszczan \& Camilo 1993, ApJ, 410, L91). We have carried out multi-frequency observations of this object at approximately bi-weekly intervals. With an rms residual in the predicted vs. observed times-of-arrival (TOAs) of $<0.5~{\rm \mu sec}$, and a large characteristic age, $\tau_c~\sim10^{10}$~yr, this object is one of the most precise celestial clocks among all known pulsars.
We detect a signature in the TOA residuals which is most naturally interpreted in terms of a general relativistic ``Shapiro Delay'', caused as the pulsar signals traverse the gravitational potential well of its $\sim 0.2~M_\odot$ companion, with the orbital angular momentum of the system lying nearly parallel to the plane of the sky. With this information we can determine the mass of the (presumed) white dwarf companion star, and the inclination angle of the orbit. Knowing the pulsar mass function (0.0079~$M_\odot$), we can in turn determine the mass of the pulsar itself. This measurement is important, among other reasons, for comparisons against the evolutionary scenarios that predict substantial mass accretion by the pulsar as it is spun up to millisecond periods by mass transfer from its companion in a low mass x-ray binary phase.
