  Electron transport is conventionally determined by the momentum-relaxing
scattering of electrons by the host solid and its excitations. The electrical
resistance is set by geometrical factors and the resistivity, which is a
microscopic property of the solid. Hydrodynamic fluid flow through channels, in
contrast, is determined by geometrical factors, boundary scattering and the
viscosity of the fluid, which is governed by momentum-conserving internal
collisions. A long-standing question in the physics of solids, brought into
focus by the advent of new calculational techniques, has been whether the
viscosity of the electron fluid plays an observable role in determining the
resistance. At first sight this seems unlikely, because in almost all known
materials the rate of momentum-relaxing collisions dominates that of the
momentum-conserving ones that give the viscous term. Here, we show this is not
always the case. We report experimental evidence that the resistance of
restricted channels of the ultra-pure two-dimensional metal PdCoO$_2$ has a
large viscous contribution. Comparison with theory allows an estimate of the
electronic viscosity in the range between $6\times 10^{-3}$~kg(ms)$^{-1}$ and
$3\times 10^{-4}$~kg(ms)$^{-1}$, which brackets that of water at room
temperature.
