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π Ceti (HR 811, B7 V) has been known to be variable in its radial velocity for almost a century, but its relatively long period and small amplitude have conspired against a determination of its orbit. We have combined in an optimal fashion observations from early in this century with modern measurements to find the spectroscopic orbit with high accuracy. The orbit has a period of 7.45 years and a semiamplitude of 4.3 km/s. The measured eccentricity of e=0.00±0.07 is indistinguishable from circular, surprising for such a long period. The 76 radial velocity observations available extend over 12 cycles of the orbit.