Silveirinha and Engheta have recently proposed that electromagnetic waves can tunnel through a material with an electric permittivity (epsilon) near zero (ENZ). An ENZ material of arbitrary geometry can thus serve as a perfect coupler between incoming and outgoing waveguides with identical cross-sectional area, so long as one dimension of the ENZ is electrically small. In this Letter we present an experimental demonstration of microwave tunneling between two planar waveguides separated by a thin ENZ channel. The ENZ channel consists of a planar waveguide in which complementary split ring resonators are patterned on the lower surface. A tunneling passband is found in transmission measurements, while a two-dimensional spatial map of the electric field distribution reveals a uniform phase variation across the channel--both measurements in agreement with theory and numerical simulations.