Relativistic jets are observed throughout the Universe, strongly impacting their surrounding environments on all physical scales, from Galactic binary systems to galaxies and galaxy clusters. An important avenue to understand the formation of these jets is by characterising the systems and circumstances from which they are launched. Whenever a black hole or neutron star accretes matter, it appears to inevitably result in the launching of a jet, the only exception being the most common type of accreting neutron stars: those with strong (\(B \geq 10^{12}\) G) magnetic fields. This exception has created the paradigm that strong magnetic fields inhibit the formation of jets. Here, we report the discovery of a jet launched by a strongly-magnetised neutron star that is accreting above the Eddington limit, disproving this long-standing paradigm. The radio luminosity of the jet is two orders of magnitude fainter than seen in other neutron stars, implying an important role for the neutron star's properties in regulating jet power. This jet detection necessitates fundamental revision of current neutron star jet models and opens up new tests of jet theory for all accreting systems. It also shows that the strong magnetic fields of ultra-luminous X-ray pulsars do not prevent such sources from launching jets.