Newly formed black holes of stellar mass launch collimated outflows (jets) of ionized matter that approach the speed of light. These outflows power prompt, brief and intense flashes of γ-rays known as γ-ray bursts (GRBs), followed by longer-lived afterglow radiation that is detected across the electromagnetic spectrum. Measuring the polarization of the observed GRB radiation provides a direct probe of the magnetic fields in the collimated jets. Rapid-response polarimetric observations of newly discovered bursts have probed the initial afterglow phase, and show that, minutes after the prompt emission has ended, the degree of linear polarization can be as high as 30 per cent - consistent with the idea that a stable, globally ordered magnetic field permeates the jet at large distances from the central source. By contrast, optical and γ-ray observations during the prompt phase have led to discordant and often controversial results, and no definitive conclusions have been reached regarding the origin of the prompt radiation or the configuration of the magnetic field. Here we report the detection of substantial (8.3 ± 0.8 per cent from our most conservative simulation), variable linear polarization of a prompt optical flash that accompanied the extremely energetic and long-lived prompt γ-ray emission from GRB 160625B. Our measurements probe the structure of the magnetic field at an early stage of the jet, closer to its central black hole, and show that the prompt phase is produced via fast-cooling synchrotron radiation in a large-scale magnetic field that is advected from the black hole and distorted by dissipation processes within the jet.