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We report on the discovery of regular Doppler shifts of the pulse period of PSR J0045-7319, the only known pulsar in the Small Magellanic Cloud. Our observations imply that the pulsar is in a highly eccentric 51-day binary orbit with a companion star having mass greater than 4M$_{\odot}$. No regular eclipses of the pulsed signal are observed. Optical observations in the direction of the pulsar reveal a B star with probable mass near 10M$_{\odot}$. We conclude that the B star is the companion to the pulsar. Timing observations of PSR J0045-7319 imply that it has not been spun up by accretion from the companion. Like the PSR B1259-63 binary system, this system is a likely X-ray binary progenitor.
