  We present an epitaxial stabilization of pyrochlore Bi$_2$Rh$_2$O$_7$ on
Y-stabilized ZrO$_2$ (YSZ) (111) substrate by inserting a pyrochlore
Eu$_2$Ti$_2$O$_7$ template layer, otherwise Bi-based layered structures being
formed directly on YSZ (111) substrate. This result reveals that
"iso-structural crystal phase" plays an important role in the interfacial phase
control. The Bi$_2$Rh$_2$O$_7$ film exhibits $p$-type electrical conduction
with the lowest longitudinal resistivity ($\rho_\mathrm{xx}$) among the
reported Rh pyrochlore oxides. Such parameters as $\rho_\mathrm{xx}$, carrier
density, and mobility show almost no temperature dependence in the measured
range of 2$-$300 K, indicating Bi$_2$Rh$_2$O$_7$ as one of the rare examples of
conducting pyrochlore oxides.
