Measuring shear-wave splitting from vertical seismic profiling (VSP) data can benefit fracture and stress characterization as well as seismic processing and interpretation. The classic approach to measuring azimuthal anisotropy at depth involves layer stripping. Its inherent weakness is the need to measure and undo overburden effects before arriving at an anisotropy estimate at depth. That task is challenging when the overburden is complex and varies quickly with depth. Moreover, VSP receivers are rarely present all the way from the surface to the target. That necessitates the use of simplistic assumptions about the uninstrumented part of the overburden that limit the quality of the result. We propose a new technique for measuring shear-wave splitting at depth that does not require any knowledge of the overburden. It is based on a multicomponent version of the virtual source method in which each two-component (2-C) VSP receiver is turned into a 2-C shear source and recorded at deeper geophones. The resulting virtual data set is affected only by the properties of the medium between the receivers. A simple Alford rotation transforms the data set into fast and slow shear virtual check shots from which shear-wave splitting can be measured easily and accurately under arbitrarily complex overburden.