We have phase-connected a sequence of Rossi X-Ray Timing Explorer Proportional Counter Array observations of SGR 1806-20 covering 178 days. We find that a simple secular spin-down model does not adequately fit the data. The period derivative varies gradually during the observations between 8.1x10-11 and 11.7x10-11 s s(-1) (at its highest, approximately 40% larger than the long-term trend), while the average burst rate as seen with the Burst and Transient Source Experiment drops throughout the time interval. The phase residuals give no compelling evidence for periodicity, but more closely resemble timing noise as seen in radio pulsars. The magnitude of the timing noise, however, is large relative to the noise level typically found in radio pulsars (Delta8=4.8; frequency derivative average power approximately 7x10-20 cycles(2) s(-3)). Combining these results with the noise levels measured for some anomalous X-ray pulsars, we find that all magnetar candidates have Delta(8) values larger than those expected from a simple extrapolation of the correlation found in radio pulsars. We find that the timing noise in SGR 1806-20 is greater than or equal to the levels found in some accreting systems (e.g., Vela X-1, 4U 1538-52, and 4U 1626-67), but the spin-down of SGR 1806-20 has thus far maintained coherence over 6 yr. Alternatively, an orbital model with a period Porb=733 days provides a statistically acceptable fit to the data. If the phase residuals are created by Doppler shifts from a gravitationally bound companion, then the allowed parameter space for the mass function (small) and orbital separation (large) rule out the possibility of accretion from the companion sufficient to power the persistent emission from the SGR.