We identify a vertical extension of the red clump stars in the color magnitude diagram (CMD) of a section of the Large Magellanic Cloud (LMC). After subtracting the principal red clump component, we find a peak in the residual stellar distribution that is ~ 0.9 mag brighter than the peak of the principal red clump distribution. We consider and reject the following possible explanations for this population: inhomogeneous reddening, Galactic disk stars, random blends of red clump stars,

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... blends of red clump stars (binaries), evolution of the red clump stars, and red clump stars from a younger LMC stellar population. Combinations of these effects cannot be ruled out as the origin of this stellar population. A natural interpretation of this new population is that it consists of red clump stars that are closer to us than those in the LMC. We find corroborating evidence for this interpretation in Holtzman et al.'s (1997) Hubble Space Telescope CMD of the LMC field stars. The derived distance and projected angular surface density of these stars relative to the LMC stars (<~ 5 to 7%) are consistent with (1) models that attribute the observed microlensing lensing optical depth (Alcock et al. 1997) to a distinct foreground stellar population (Zhao 1997) and (2) tidal models of the interaction between the LMC and the Milky Way (Lin, Jones, & Klemola 1995). We conclude that the standard assumption of a smoothly distributed halo population out to the LMC cannot be substantiated without at least a detailed understanding of red clump stellar evolution, binary fractions, binary mass ratios, the spatial correlation of stars within the LMC, possible variations in the stellar populations of satellite galaxies, and differential reddening - all of which are highly complex.