  We provide evidence for a finite temperature ferromagnetic transition in
2-dimensions as $H \to 0$ in thin films of $^3$He on graphite, a model system
for the study of two-dimensional magnetism. We perform pulsed and CW NMR
experiments at fields of 0.03 - 0.48 mT on $^3$He at areal densities of 20.5 -
24.2 atoms/nm$^2$. At these densities, the second layer of $^3$He has a
strongly ferromagnetic tendency. With decreasing temperature, we find a rapid
onset of magnetization that becomes independent of the applied field at
temperatures in the vicinity of 1 mK. Both the dipolar field and the NMR
linewidth grow rapidly as well, which is consistent with a large (order unity)
polarization of the $^3$He spins.

Condensed Matter