  The prototypical delafossite metal PdCoO$_2$ has been the subject of intense
interest for hosting exotic transport properties. Using first-principles
transport calculations and theoretical modeling, we reveal that the high
electrical conductivity of PdCoO$_2$ at room temperature originates from the
contributions of both high Fermi velocities, enabled by Pd $4d_{z^2}-5s$
hybridization, and exceptionally weak electron-phonon coupling, which leads to
a coupling strength ($\lambda=0.057$) that is nearly an order of magnitude
smaller than those of common metals. The abnormally weak electron-phonon
coupling in PdCoO$_2$ results from a low electronic density of states at the
Fermi level, as well as the large and strongly facetted Fermi surface with
suppressed Umklapp electron-phonon matrix elements. We anticipate that our work
will inform the design of unconventional metals with superior transport
properties.
