Germanium-tin alloy nanowires hold promise as silicon-compatible optoelectronic elements with the potential to achieve a direct band gap transition required for efficient light emission. In contrast to GeSn epitaxial thin films, free-standing nanowires deposited on misfitting germanium or silicon substrates can avoid compressive, elastic strains that inhibit formation of a direct gap. We demonstrate strong room temperature photoluminescence, consistent with band edge emission from both Ge core nanowires, elastically strained in tension, and the almost unstrained GeSn shells grown around them. Low-temperature chemical vapor deposition of these core-shell structures was achieved using standard precursors, resulting in Sn incorporation that significantly exceeds the bulk solubility limit in germanium.