Near a black hole, differential rotation of a magnetized accretion disk is thought to produce an instability that amplifies weak magnetic fields, driving accretion and outflow. These magnetic fields would naturally give rise to the observed synchrotron emission in galaxy cores and to the formation of relativistic jets, but no observations to date have been able to resolve the expected horizonscale magnetic-field structure. We report interferometric observations at 1.3-millimeter wavelength that spatially resolve the linearly polarized emission from the Galactic Center supermassive black hole, Sagittarius A*. We have found evidence for partially ordered fields near the event horizon, on scales of ∼6 Schwarzschild radii, and we have detected and localized the intra-hour variability associated with these fields.Sagittarius A* (Sgr A * ) emits most of its ∼10 36 erg/s luminosity at wavelengths just short of one millimeter, resulting in a distinctive "submillimeter bump" in its spectrum (1). A diversity of models attribute this emission to synchrotron radiation from a population of relativistic thermal electrons in the innermost accretion flow (2-4). Such emission is expected to be strongly linearly polarized, ∼70% in the optically thin limit for a highly ordered magnetic field configuration (5), with its direction tracing the underlying magnetic field. At 1.3-mm wavelength, models of magnetized accretion flows predict linear polarization fractions > ∼ 30% (6-9), yet connected-element interferometers measure only a 5−10% polarization fraction for Sgr A * (10, 11), typical for galaxy cores (12). However, the highest resolutions of these instruments, ∼0.1−1 , are insufficient to resolve the millimeter emission region, and linear polarization is not detected from Sgr A * at the longer wavelengths where facility verylong-baseline interferometry (VLBI) instruments offer higher resolution (13). Thus, these low polarization fractions could indicate any combination of low intrinsic polarization, depolarization from Faraday rotation or opacity, disordered magnetic fields within the turbulent emitting 2 plasma, or ordered magnetic fields with unresolved structure leading to a low beam-averaged polarization. The higher polarization seen during some near-infrared flares may support the last possibility (14, 15), but the origin and nature of these flares is poorly understood, and they may probe a different emitting electron population than is responsible for the energetically dominant submillimeter emission.To definitively study this environment, we are assembling the Event Horizon Telescope (EHT), a global VLBI array operating at 1.3-mm wavelength. Initial studies with the EHT have spatially resolved the ∼40 microarcsecond (µas) emission region of Sgr A * (16, 17), suggesting the potential for polarimetric VLBI with the EHT to resolve its magnetic field structure. On longer baselines,m mixes information about the spatial distribution of polarization with information about the strength and direction of polarization and must be in...