Accretion disks in strong gravity ubiquitously produce winds, seen as blueshifted absorption lines in the X-ray band of both stellar mass X-ray binaries (black holes and neutron stars) ^1–4 and supermassive black holes ⁵ . Some of the most powerful winds (termed Eddington winds) are expected to arise from systems in which radiation pressure is sufficient to unbind material from the inner disk ( L ≳ L _Edd ). These winds should be extremely fast and carry a large amount of kinetic power, which, when associated with supermassive black holes, would make them a prime contender for the feedback mechanism linking the growth of those black holes with their host galaxies ⁶ . Here we show the XRISM Resolve spectrum of the galactic neutron star X-ray binary, GX 13+1, which reveals one of the densest winds ever seen in absorption lines. This Compton-thick wind significantly attenuates the flux, making it appear faint, although it is intrinsically more luminous than usual ( L ≳ L _Edd ). However, the wind is extremely slow, more consistent with the predictions of thermal-radiative winds launched by X-ray irradiation of the outer disk than with the expected Eddington wind driven by radiation pressure from the inner disk. This puts new constraints on the origin of winds from bright accretion flows in binaries, but also highlights the very different origin required for the ultrafast ( v ~ 0.3 c ) winds seen in recent Resolve observations of a supermassive black hole at a similarly high Eddington ratio ⁷ .