A small fraction of galaxies appear to reside in dense compact groups, whose inferred crossing times are much shorter than a Hubble time. These short crossing times have led to considerable disagreement about the dynamical state of these systems. We suggest that many of the observed groups are not physically bound but are chance projections of galaxies well-separated along the line of sight. Unlike earlier similar proposals, ours does not require that the galaxies in the compact group be

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... of a more diffuse, but physically bound entity. The probability of physically separated galaxies projecting into an apparent compact group is non-negligible if most galaxies are distributed, as observed, in thin filaments. We illustrate this general point with a specific example: a simulation of a cold dark matter universe, in which hydrodynamic effects are included to identify galaxies. The simulated galaxy distribution is filamentary, and end-on views of these filaments produce apparent galaxy associations that have sizes and velocity dispersions similar to those of observed compact groups. The frequency of such projections can explain the observed space-density of groups in the Hickson catalog. We discuss the implications of our proposal for the formation and evolution of groups and elliptical galaxies. The proposal can be tested by using redshift-independent distance estimators to measure the line-of-sight spatial extent of nearby compact groups.