  We report clear experimental signatures of the theoretically unexpected
gas-liquid transition in the first three monolayers of $^3$He adsorbed on
graphite. The transition is inferred from the linear density dependence of the
$\gamma$-coefficient of the heat capacity measured in the degenerate region (2
$\le T \le$80 mK) below a critical liquid density ($\rho_{c0}$). Surprisingly,
the measured $\rho_{c0}$ values (0.6$\sim$0.9 nm$^{-2}$) are nearly the same
for all these monolayers in spite of their quite different environments. We
conclude that the ground-state of $^3$He in strict two dimensions is not a
dilute quantum gas but a self-bound quantum liquid with the lowest density ever
found.
