We present an analysis of the unusual optical light curve of the gamma-ray burst GRB 081029, a long-soft burst with a redshift of z = 3.8479. We combine X-ray and optical observations from the Swift X-Ray Telescope and the Swift UltraViolet/Optical Telescope with ground-based optical and infrared data obtained using the REM, ROTSE, and CTIO 1.3 m telescopes to construct a detailed data set extending from 86 s to similar to 100000 s after the BAT trigger. Our data cover a wide energy range from 10 keV to 0.77 eV (1.24 angstrom-16000 angstrom). The X-ray afterglow shows a shallow initial decay followed by a rapid decay starting at about 18000 s. The optical and infrared afterglow, however, shows an uncharacteristic rise at about 3000 s that does not correspond to any feature in the X-ray light curve. Our data are not consistent with synchrotron radiation from a jet interacting with an external medium, a two-component jet, or continuous energy injection from the central engine. We find that the optical light curves can be broadly explained by a collision between two ejecta shells within a two-component jet. A growing number of gamma-ray-burst afterglows are consistent with complex jets, which suggests that some (or all) gamma-ray-burst jets are complex and will require detailed modeling to fully understand them.