We present photoluminescence (PL) spectroscopy measurements of single-layer MoSe2 as a function of uniform uniaxial strain. A simple clamping and bending method is described that allows for application of uniaxial strain to layered, 2D materials with strains up to 1.1% without slippage. Using this technique, we find that the electronic band gap of single layer MoSe2 can be reversibly tuned by -27 ± 2 meV per percent of strain. This is in agreement with our density-functional theory calculations, which estimate a modulation of -32 meV per percent of strain, taking into account the role of deformation of the underlying substrate upon bending. Finally, due to its narrow PL spectra as compared with that of MoS2, we show that MoSe2 provides a more precise determination of small changes in strain making it the ideal 2D material for strain applications.