A new effect is described by which primordial gravity waves leave a permanent signature in the large scale structure of the Universe. The effect occurs at second order in perturbation theory and is sensitive to the order in which perturbations on different scales are generated. We derive general forecasts for the detectability of the effect with future experiments and consider observations of the prereionization gas through the 21 cm line. It is found that the Square Kilometer Array will not be competitive with current cosmic microwave background constraints on primordial gravity waves from inflation. However, a more futuristic experiment could, through this effect, provide the highest ultimate sensitivity to tensor modes and possibly even measure the tensor spectral index. It is thus a potentially quantitative probe of the inflationary paradigm.