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We report rf-penetration depth measurements of the quasi-2D organic superconductor β″-(BEDT-TTF)2[(H2O)(NH4)2Cr(C2O4)3]·18-crown-6, which has the largest separation between consecutive conduction layers of any 2D organic metal with a single packing motif. Using a contactless tunnel diode oscillator measurement technique, we show the zero-field cooling dependence and field sweeps up to 28 T oriented at various angles with respect to the crystal conduction planes. When oriented parallel to the layers, the upper critical field, Hc2=7.6 T, which is the calculated paramagnetic limit for this material. No signs of inhomogeneous superconductivity are seen, despite previous predictions. When oriented perpendicular to the layers, Shubnikov–de Haas oscillations are seen as low as 6 T, and from these we calculate Fermi surface parameters such as the superconducting coherence length and Dingle temperature. One remarkable result from our data is the high anisotropy of Hc2 in the parallel and perpendicular directions, due to an abnormally low Hc2⊥=0.4 T. Such high anisotropy is rare in other organics and the origin of the smaller Hc2⊥ may be a consequence of a lower effective mass.