Thin, flexible and invisible solar cells will be an ubiquitous technology in the near future. Ultrathin crystalline silicon (c-Si) cells capitalise on the success of bulk silicon cells while being light-weight and mechanically flexible, but suffer from poor absorption and efficiency. Here we present a new family of surface texturing, based on correlated disordered hyperuniform patterns, capable of efficiently coupling the incident spectrum into the silicon slab optical modes. We experimentally demonstrate 66.5% solar light absorption in free-standing 1 µm c-Si layers by hyperuniform nanostructuring. The absorption equivalent photocurrent derived from our measurements is 26.3 mA/cm2, which is far above the highest found in literature for Si of similar thickness. Considering state-of-the-art Si PV technologies, the enhanced light trapping translates to a record efficiency above 15%. The light absorption can potentially be increased up to 33.8 mA/cm2 by incorporating a back-reflector and improved anti-reflection, for which we estimate a photovoltaic efficiency above 21% for 1 µm thick Si cells.