Here, we propose a strain gauge based on single-layer MoSe2 and WSe2 and show that, in these materials, the strain induced modulation of inter-valley phonon scattering leads to large mobility changes, which in turn result in highly sensitive strain gauges. By employing density-functional theory bandstructure calculations, comprehensive scattering models, and the linearized Boltzmann equation, we explain the physical mechanisms for the high sensitivity to strain of the resistivity in single-layer MoSe2 and WSe2, discuss the reduction of the gauge factor produced by extrinsic scattering sources (e.g., chemical impurities), and propose ways to mitigate such sensitivity degradation.