Dislocations, one-dimensional lattice imperfections, are common to technologically important materials such as III-V semiconductors, and adversely affect heat dissipation in, for example, nitride-based high-power electronic devices. For decades, conventional nonlinear elasticity models have predicted that this thermal resistance is only appreciable when the heat flux is perpendicular to the dislocations. However, this dislocation-induced anisotropic thermal transport has yet to be seen experimentally. Using time-domain thermoreflectance, we measure strong thermal transport anisotropy governed by highly oriented threading dislocation arrays throughout micrometre-thick, single-crystal indium nitride films. We find that the cross-plane thermal conductivity is almost tenfold higher than the in-plane thermal conductivity at 80 K when the dislocation density is ~3 × 1010 cm-2. This large anisotropy is not predicted by conventional models. With enhanced understanding of dislocation-phonon interactions, our results may allow the tailoring of anisotropic thermal transport with line defects, and could facilitate methods for directed heat dissipation in the thermal management of diverse device applications.