We report on the results of an I-band photometric variability survey of eighteen L dwarfs. We find that seven exhibit statistically significant variations above the 95.4% confidence level with root-mean-square scatter (including photometric errors) between 0.010 and 0.083 mag. Another five targets have variability probabilities ~80%, suggesting that these are likely variable objects. Three of the variable objects display significant peaks in a CLEAN periodogram that are several times higher than the noise. The period for 2MASS 0345+25 is clearly not intrinsic to the object and can be dismissed. The periods found for 2MASS 0746+20AB and 2MASS 1300+19 are unique but longer than those periods likely from rotation velocity measurements and they do not represent periodic behavior in the light curve that persists through the entire data set. These observations suggest that we are not observing the rotation modulation of a long-lived albedo feature. Instead, rapid evolution of atmospheric features is likely causing the non-periodic variability. The remaining variable objects show no prominent features in their light curves, suggesting even more rapid evolution of atmospheric features. We argue against the existence of magnetic spots in these atmospheres and favor the idea that non-uniform condensate coverage is responsible for these variations. The magnetic Reynolds number in the atmosphere of L dwarfs is too small to support the formation of magnetic spots. In contrast, silicate and iron clouds are expected to form in the photospheres of L dwarfs. Inhomogeneities in such cloud decks and the evolution of the inhomogeneities can plausibly produce the observed photometric variations.

42 pages, 14 figures, minor corrections for typos and Figure 12, to appear in ApJ, v577, September 20, 2002