  In complementary images of coordinate-space and momentum-space density in a
trapped 2D Bose gas, we observe the emergence of pre-superfluid behavior. As
phase-space density $\rho$ increases toward degenerate values, we observe a
gradual divergence of the compressibility $\kappa$ from the value predicted by
a bare-atom model, $\kappa_{ba}$. $\kappa/\kappa_{ba}$ grows to 1.7 before
$\rho$ reaches the value for which we observe the sudden emergence of a spike
at $p=0$ in momentum space. Momentum-space images are acquired by means of a 2D
focusing technique. Our data represent the first observation of non-meanfield
physics in the pre-superfluid but degenerate 2D Bose gas.
