We report the serendipitous discovery of a late-type giant star that exhibited a smooth, eclipse-like drop in flux to a depth of 97 per cent. Minimum flux occurred in April 2012 and the total event duration was a few hundred days. Light curves in V, I and K_s from the Optical Gravitational Lensing Experiment and VISTA Variables in the Via Lactea surveys show a remarkably achromatic event. During 17 years of observational coverage of this source only one such event was detected. The physical properties of the giant star itself appear somewhat unusual, which may ultimately provide a clue towards the nature of the system. By modelling the event as an occultation by an object that is elliptical in projection with uniform transparency, we place limits on its physical size and velocity. We find that the occultation is unlikely to be due to a chance alignment with a foreground object. We consider a number of possible candidates for the occulter, which must be optically thick and possess a radius or thickness in excess of 0.25 au. None are completely satisfactory matches to all the data. The duration, depth and relative achromaticity of the dip mark this out as an exceptionally unusual event, whose secret has still not been fully revealed. We find two further candidates in the VVV survey and we suggest that these systems, and two previously known examples, may point to a broad class of long period eclipsing binaries wherein a giant star is occulted by a circumsecondary disc.