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.
