Recent progress in inflationary model-building in string theory has revealed a spectrum of scenarios with disparate phenomenology. However, few, if any, of these constructions can produce an observably large primordial tensor signal in the CMB. Detecting such a signal would give important clues about physics at the Planck scale. I will explain why string theory does not readily produce such a signal, and how a detection would exclude nearly all models of D-brane inflation, as well as most closed string models. I will then describe one possible way to evade these obstacles and produce a tensor signal in string theory.