With the surge of research in quantum information, the issue of producing entangled states has gained prominence. Here, we show that judiciously bringing together two systems of strongly interacting electrons with vastly differing ground states-the gapped BCS superconductor and the Luttinger liquid-can result in quantum entanglement. We propose three sets of measurements involving single-walled metallic carbon nanotubes which have been shown to exhibit Luttinger liquid physics, to test our claim and as nanoscience experiments of interest in and of themselves.