  The viscosity is measured for a Fermi liquid, a dilute $^3$He-$^4$He mixture,
under extremely high magnetic field/temperature conditions ($B \leq 14.8$ T, $T
\geq 1.5$ mK). The spin splitting energy $\mu B$ is substantially greater than
the Fermi energy $k_B T_F$; as a consequence the polarization tends to unity
and s-wave quasiparticle scattering is suppressed for $T \ll T_F$. Using a
novel composite vibrating-wire viscometer an enhancement of the viscosity is
observed by a factor of more than 500 over its low-field value. Good agreement
is found between the measured viscosity and theoretical predictions based upon
a $t$-matrix formalism.
