A Ti-29 wt % Mg (Ti-45 at % Mg) alloy produced by vapour quenching has been studied using scanning electron microscopy, transmission electron microscopy, energy dispersive X-ray spectroscopy, imaging parallel electron energy-loss spectroscopy and electron diffraction. The alloy is shown to be composed of highly supersaturated solid solutions between two elements hitherto believed to be immiscible. It has a microstructure consisting of columnar units, columnar grains, columnar subgrains, herring-bone patterns and parallel stripes ranging in size from 15 mu m to 2 nm. Superimposed on the microstructure are periodic compositional bands with a period of similar to 0.5 mu m. The origins of the periodic compositional bands and the herring-bone patterns are discussed.