Line intensity mapping experiments seek to trace large scale structure by measuring the spatial fluctuations in the combined emission, in some convenient spectral line, from individually unresolved galaxies. An important systematic concern for these surveys is line confusion from foreground or background galaxies emitting in other lines that happen to lie at the same observed frequency as the target emission line of interest. We develop an approach to separate this interloper emission at the power spectrum level. If one adopts the redshift of the target emission line in mapping from observed frequency and angle on the sky to co-moving units, the interloper emission is mapped to the wrong co-moving coordinates. Since the mapping is different in the line of sight and transverse directions, the interloper contribution to the power spectrum becomes anisotropic, especially if the interloper and target emission are at widely separated redshifts. This distortion is analogous to the Alcock-Paczynski test, but here the warping arises from assuming the wrong redshift rather than an incorrect cosmological model. We apply this to the case of a hypothetical [CII] emission survey at z~7 and find that the distinctive interloper anisotropy can, in principle, be used to separate strong foreground CO emission fluctuations. In our models, however, a significantly more sensitive instrument than currently planned is required, although there are large uncertainties in forecasting the high redshift [CII] emission signal. With upcoming surveys, it may nevertheless be useful to apply this approach after first masking pixels suspected of containing strong interloper contamination.
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