We present results on the growth of CdTe-HgTe core-shell nanowires, a realization of a quasi one-dimensional heterostructure of the topological insulator HgTe. The growth is a two step process consisting of the growth of single crystalline zinc blende CdTe nanowires with the vapor-liquid-solid method and the overgrowth of these wires with HgTe such that a closed shell is formed around the CdTe core structure. The CdTe wire growth is monitored by RHEED allowing us to infer information on the crystal properties from the electron diffraction pattern. This information is used to find and control the optimal growth temperature. High quality single crystal CdTe nanowires grow with a preferred orientation. For the growth of the conductive HgTe shell structure we find that the supplied Hg:Te ratio is the crucial parameter to facilitate growth on all surface facets.