A two-step deposition process was developed in a metal organic chemical vapor deposition system to create a defect-free p-type structure consisting of a GaN nanowire (NW) core surrounded by a distinct AlGaN radial shell. The m-plane growth direction yields a nanowire with an isosceles triangular cross section with two identical {-110-1} facets and a third (0001) facet. The AlGaN shell introduces a polarization-induced sheet charge at the AlGaN/GaN interface and may shield the NW from surface-state induced depletion. Transmission electron microscopy confirmed that single-component NWs and sufficiently thin NW heterostructures are free of extended defects. High hole currents and current modulation were demonstrated with back-gated NW transistor structures.