  Using a novel technique, we make quantitative measurements of the spin
polarization of dilute (3.4 to 6.8*10^{10} cm^{-2}) GaAs (311)A two-dimensional
holes as a function of an in-plane magnetic field. As the field is increased
the system gradually becomes spin polarized, with the degree of spin
polarization depending on the orientation of the field relative to the crystal
axes. Moreover, the behavior of the system turns from metallic to insulating
\textit{before} it is fully spin polarized. The minority-spin population at the
transition is ~8*10^{9} cm^{-2}, close to the density below which the system
makes a transition to an insulating state in the absence of a magnetic field.
