A search for periodic variation in the production of gas and dust by Comet Halley has been performed using narrowband photometric measurements from four sites - Lowell Observatory, Mauna Kea Observatory, Perth Observatory, and Cerro Tololo Inter-American Observatory. The method of phase dispersion minimization was applied to observations made during 164 observing nights between September 1985 and June 1986. A clear-cut variation, with a period near 7.4 days, was present throughout the postperihelion window. Less conclusive evidence of a similar period has been found in the pre-perihelion data. No indication of a shorter period or of strong sporadic activity exists in the data. The observations require that Halley's nucleus returns to essentially the same orientation with respect to the sun approximately every 7.4 days except for longer-timescale seasonal evolution. This fact precludes certain proposed models of nuclear motion.