The viscosity is measured for a Fermi liquid, a dilute 3He-4He mixture, under extremely high magnetic field/temperature conditions (B≤14.8  T, T≥1.5  mK). The spin-splitting energy μB is substantially greater than the Fermi energy kBTF; as a consequence the polarization tends to unity and s-wave quasiparticle scattering is suppressed for T≪TF. 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.