We identify nine young stellar objects (YSOs) in the NGC 2264 star-forming region with optical {em CoRoT} light curves exhibiting short-duration, shallow, periodic flux dips. All of these stars have infrared (IR) excesses that are consistent with their having inner disk walls near the Keplerian co-rotation radius. The repeating photometric dips have FWHM generally less than one day, depths almost always less than 15%, and periods (3<P<11 days) consistent with dust near the Keplerian co-rotation period. The flux dips vary considerably in their depth from epoch to epoch, but usually persist for several weeks and, in two cases, were present in data collected on successive years. For several of these stars, we also measure the photospheric rotation period and find that the rotation and dip periods are the same, as predicted by standard disk-locking models. We attribute these flux dips to clumps of material in or near the inner disk wall, passing through our line of sight to the stellar photosphere. In some cases, these dips are also present in simultaneous {em Spitzer} IRAC light curves at 3.6 and 4.5 microns. We characterize the properties of these dips, and compare the stars with light curves exhibiting this behavior to other classes of YSO in NGC 2264. A number of physical mechanisms could locally increase the dust scale height near the inner disk wall, and we discuss several of those mechanisms; the most plausible mechanisms are either a disk warp due to interaction with the stellar magnetic field or dust entrained in funnel-flow accretion columns arising near the inner disk wall.
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