In complementary images of coordinate-space and momentum-space density in a trapped 2D Bose gas, we observe the emergence of presuperfluid behavior. As phase-space density ρ increases toward degenerate values, we observe a gradual divergence of the compressibility κ from the value predicted by a bare-atom model, κ ba . κ/κ ba grows to 1.7 before ρ 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-mean-field physics in the presuperfluid but degenerate 2D Bose gas.PACS numbers: 05.30. Jp, 67.10.Ba, Because of the enhanced role of fluctuations in lowdimensional systems [1], a two-dimensional (2D) Bose gas at nonzero temperature does not have long-range phase coherence. In a homogeneous system there can be at best only a quasicondensate, no true Bose-Einstein condensation (BEC). Under the combined effect of interactions and quantum degeneracy, however, there is nonetheless a phase transition known as Berezinskii-KosterlitzThouless (BKT) associated with the unbinding of vortex pairs [2]. Below the critical temperature T BKT , the system is superfluid.Experiments in 2D atomic gases [3][4][5][6] are usually conducted in the presence of an inhomogeneous trapping potential. In the complete absence of interactions, the confining potential can resurrect a traditional BEC [7], but for realistic experimental parameters, interatomic interactions tend to suppress BEC by smoothing out the spatial profile [3-6, 8, 9] of the mean density to the point where the sample can be understood as a collection of locally uniform spatial regions, each of which is characterized by a particular local density and thus a particular local value of T BKT . Although these local regions may be too small to test in detail the coherence-related predictions of BKT theory, qualitative effects have been observed in experiment [3,6].Our particular interest is in the region just to the warm side of T BKT . In an earlier experiment on bosons trapped in a 2D optical lattice, we observed a proliferation of vortices as we warmed through the discrete-case equivalent of T BKT [10]. But in that experiment a great many mesoscopic condensates were present, one at each lattice site, on both sides of the BKT transition, because they had condensed at a T BEC distinct from and well above T BKT . For the continuous case, in contrast, there is no corresponding second transition temperature above T BKT . But if the cooling gas has by T BKT already become a medium that can support vortices, whether bound or not, then heuristically we see that it must have continuously evolved from a fully fluctuating nondegenerate gas into a sort of presuperfluid with suppressed density fluctuations [11]. Theory [8,[11][12][13][14][15] validates this intuition, and experiments [5] have in turn been consistent with predictions of that theory. Up until now, however, experiments have not been directly sensitive to the proper...