C60-based solids1 are archetypal molecular superconductors with transition temperatures (Tc) as high as 33 K (refs 2–4). Tc of face-centred-cubic (f.c.c.) A3C60 (A=alkali metal) increases monotonically with inter C60 separation, which is controlled by the A+ cation size. As Cs+ is the largest such ion, Cs3C60 is a key material in this family. Previous studies revealing trace superconductivity in CsxC60 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 Cs3C60 can be reproducibly isolated by solvent-controlled synthesis and has the highest Tc of any molecular material at 38 K. In contrast to other A3C60 materials, two distinct cubic Cs3C60 structures are accessible. Although f.c.c. Cs3C60 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 Cs3C60 from insulating at ambient pressure to superconducting without crystal structure change and reveals a broad maximum in Tc at 7 kbar. We attribute the observed Tc maximum as a function of inter C60separation—unprecedented in fullerides but reminiscent of the atom-based cuprate superconductors—to the role of strong electronic correlations near the metal–insulator transition onset.