Cosmic-ray acceleration has been a long-standing mystery and despite more than a century of study, we still do not have a complete census of acceleration mechanisms. The collision of strong stellar winds in massive binary systems creates powerful shocks, which have been expected to produce high-energy cosmic-rays through Fermi acceleration at the shock interface. The accelerated particles should collide with stellar photons or ambient material, producing non-thermal emission observable in X-rays and gamma-rays. The supermassive binary star eta Carinae drives the strongest colliding wind shock in the solar neighborhood. Observations with non-focusing high-energy observatories indicate a high energy source near eta Carinae, but have been unable to conclusively identify eta Carinae as the source because of their relatively poor angular resolution. Here we present the first direct focussing observations of the non-thermal source in the extremely hard X-ray band, which is found to be spatially coincident with the star within several arc-seconds. These observations show that the source of non-thermal X-rays varies with the orbital phase of the binary, and that the photon index of the emission is similar to that derived through analysis of the gamma-ray spectrum. This is conclusive evidence that the high-energy emission indeed originates from non-thermal particles accelerated at colliding wind shocks.