  In this letter we report on proximity superconductivity induced in CdTe-HgTe
core-shell nanowires, a quasi-one-dimensional heterostructure of the
topological insulator HgTe. We demonstrate a Josephson supercurrent in our
nanowires contacted with superconducting Al leads. The observation of a sizable
$I_c R_n$ product, a positive excess current and multiple Andreev reflections
up to fourth order further indicate a high interface quality of the junctions.
