We present new deep near-infrared images of dark clouds in the Perseus molecular complex. These images show beautiful extended emission which we model as scattered ambient starlight and name ``cloudshine. The brightness and color variation of cloudshine complicates the production of extinction maps, the best tracer of column density in clouds. However, since the profile of reflected light is essentially a function of mass distribution, cloudshine provides a new way to study the structure of dark clouds. Previous work has used optical scattered light to study the density profile of tenuous clouds; extending this technique into the infrared provides a high-resolution view into the interiors of very dense clouds, bypassing the complexities of using thermal dust emission, which is biased by grain temperature, or molecular tracers, which have complicated depletion patterns. As new wide-field infrared cameras are used to study star-forming regions at greater depth, cloudshine will be widely observed and should be seen as a new high-resolution tool, rather than an inconvenience.