Context. A stellar occultation by a trans-Neptunian object (TNO) provides an opportunity to probe the size and shape of these distant solar system bodies. In the past seven years, several occultations by TNOs have been observed, but mostly from a single location. Only very few TNOs have been sampled simultaneously from multiple locations. Sufficient data that enable a robust estimation of shadow size through an ellipse fit could only be obtained for two objects. Aims. We present the first observation of an occultation by the TNO 2007 UK sub(126) on 15 November 2014, measured by three observers, one nearly on and two almost symmetrical to the shadow's centerline. This is the first multi-chord dataset obtained for a so-called detached object, a TNO subgroup with perihelion distances so large that the giant planets have likely not perturbed their orbits. We also revisit Herschel/PACS far-infrared data, applying a new reduction method to improve the accuracy of the measured fluxes. Combining both datasets allows us to comprehensively characterize 2007 UK sub(126). Methods. We use error-in-variable regression to solve the non-linear problem of propagating timing errors into uncertainties of the ellipse parameters. Based on the shadow's size and a previously reported rotation period, we expect a shape of a Maclaurin spheroid and derive a geometrically plausible size range. To refine our size estimate of 2007 UK sub(126), we model its thermal emission using a thermophysical model code. We conduct a parametric study to predict far-infrared fluxes and compare them to the Herschel/PACS measurements. Results. The favorable geometry of our occultation chords, combined with minimal dead-time imaging, and precise GPS time measurements, allow for an accurate estimation of the shadow size (best-fitting ellipse with axes 645.80 + or - 5.68 km x 597.81 + or - 12.74 km) and the visual geometric albedo (pV= 15.0 + or - 1.6%). By combining our analyses of the occultation and the far-infrared data, we can constrain the effective diameter of 2007 UK sub(126) to d sub(eff)= 599-629 km. We conclude that subsolar surface temperatures are in the order of approximate 50-55 K.