Abstract: We present results from spectral fitting of the very high state of GX339-4 with Nuclear Spectroscopic Telescope Array (NuSTAR) and Swift. We use relativistic reflection modeling to measure the spin of the black hole and inclination of the inner disk and find a spin of a = 0.95+0.08/-0.02 and inclination of 30deg +/- 1deg (statistical errors). These values agree well with previous results from reflection modeling. With the exceptional sensitivity of NuSTAR at the high-energy side of the disk s…