We report our analysis of the stability of pulsation periods in the DAV star (pulsating hydrogen atmosphere white dwarf) ZZ Ceti, also called R548. On the basis of observations that span 31 years, we conclude that the period 213.13 s observed in ZZ Ceti drifts at a rate dP/dt<=(5.5+/-1.9)×10-15 s s-1, after correcting for proper motion. Our results are consistent with previous P values for this mode and an improvement over them because of the larger time base. The characteristic stability timescale implied for the pulsation period is |P/P|>=1.2 Gyr, comparable to the theoretical cooling timescale for the star. Our current stability limit for the period 213.13 s is only slightly less than the present measurement for another DAV, G117-B15A, for the period 215.2 s, establishing this mode in ZZ Ceti as the second most stable optical clock known, comparable to atomic clocks and more stable than most pulsars. Constraining the cooling rate of ZZ Ceti aids theoretical evolutionary models and white dwarf cosmochronology. The drift rate of this clock is small enough that we can set interesting limits on reflex motion due to planetary companions.