  We present the first experimental investigation of modulational instability
in a layered Kerr medium. The particularly interesting and appealing feature of
our configuration, consisting of alternating glass-air layers, is the
piecewise-constant nature of the material properties, which allows a
theoretical linear stability analysis leading to a Kronig-Penney equation whose
forbidden bands correspond to the modulationally unstable regimes. We find very
good {\it quantitative} agreement between theoretical, numerical, and
experimental diagnostics of the modulational instability. Because of the
periodicity in the evolution variable arising from the layered medium, there
are multiple instability regions rather than just one as in the uniform medium.
