We report our analysis of the stability of pulsation periods in the DAV star (pulsating hydrogen atmosphere white dwarf) ZZ Ceti, also called R 548. Based on observations that span 31 years, we conclude that the period 213.132605 s observed in ZZ Ceti drifts at a rate dP/dt<=(5.5+/-1.9)times 10-15 s/s, after correcting for proper motion. Our results are consistent with previous Pdot values for this mode and an improvement over them due to the larger time-base. The characteristic stability timescale implied for the pulsation period is mid P/Pdot mid >=1.2 Gyr, comparable to the theoretical cooling timescale for the star. Our current stability limit for the period 213.132605 s is only slightly less than the present measurement for G 117-B15A for the period 215.2 s, another DAV, establishing this mode in ZZ Ceti as the second most stable optical clock known, more stable than atomic clocks and 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 reflex motion caused by any orbital planets is detectable within limits; our dot {P} constraint places limits on the mass and/or distance of any orbital companions.