  We theoretically investigate the transmission of electromagnetic radiation
through a metal plate with a zero-$\epsilon$ metamaterial slit, where the
permittivity tends towards zero over a given bandwidth. Our analytic results
demonstrate that the transmission coefficient can be substantial for a broad
range of slit geometries, including subwavelength widths that are many
wavelengths long. This novel resonant effect has features quite unlike the
Fabry-P\'{e}rot-like resonances that have been observed in conductors with deep
channels. We further reveal that these high impedance ultranarrow
zero-$\epsilon$ channels can have significantly {\it greater} transmission
compared to slits with no wave impedance difference across them.
