C(60)-based solids are archetypal molecular superconductors with transition temperatures (Tc) as high as 33 K (refs 2-4). Tc of face-centred-cubic (f.c.c.) A(3)C(60) (A=alkali metal) increases monotonically with inter C(60) separation, which is controlled by the A(+) cation size. As Cs(+) is the largest such ion, Cs(3)C(60) is a key material in this family. Previous studies revealing trace superconductivity in Cs(x)C(60) materials have not identified the structure or composition of the superconducting phase owing to extremely small shielding fractions and low crystallinity. Here, we show that superconducting Cs(3)C(60) can be reproducibly isolated by solvent-controlled synthesis and has the highest Tc of any molecular material at 38 K. In contrast to other A(3)C(60) materials, two distinct cubic Cs(3)C(60) structures are accessible. Although f.c.c. Cs(3)C(60) can be synthesized, the superconducting phase has the A15 structure based uniquely among fullerides on body-centred-cubic packing. Application of hydrostatic pressure controllably tunes A15 Cs(3)C(60) from insulating at ambient pressure to superconducting without crystal structure change and reveals a broad maximum in Tc at approximately 7 kbar. We attribute the observed Tc maximum as a function of inter C(60)separation--unprecedented in fullerides but reminiscent of the atom-based cuprate superconductors--to the role of strong electronic correlations near the metal-insulator transition onset.