We have conducted a photometric monitoring program of 3 field late-L brown dwarfs looking for evidence of non-axisymmetric structure or temporal variability in their photospheres. The observations were performed using Spitzer/IRAC 4.5 and 8 micron bandpasses and were designed to cover at least one rotational period of each object. One-sigma RMS (root mean squared) uncertainties of less than 3 mmag at 4.5 micron and around 9 mmag at 8 micron were achieved. Two out of the three objects studied exhibit some modulation in their light curves at 4.5 micron - but not 8 micron - with periods of 7.4 hr and 4.6 hr and peak-to-peak amplitudes of 10 mmag and 8 mmag. Although the lack of detectable 8 micron variation suggests an instrumental origin for the detected variations, the data may nevertheless still be consistent with intrinsic variability since the shorter wavelength IRAC bandpasses probe more deeply into late L dwarf atmospheres than the longer wavelengths. A cloud feature occupying a small percentage (1-2 %) of the visible hemisphere could account for the observed amplitude of variation. If, instead, the variability is indeed instrumental in origin, then our non-variable L dwarfs could be either completely covered with clouds or objects whose clouds are smaller and uniformly distributed. Such scenarios would lead to very small photometric variations. Followup IRAC photometry at 3.6 and 5.8 micron bandpasses should distinguish between the two cases. In any event, the present observations provide the most sensitive search to date for structure in the photospheres of late-L dwarfs at mid-IR wavelengths, and our photometry provides stringent upper limits to the extent to which the photospheres of these transition L dwarfs are structured.