The brightness of the night sky at an astronomical site is one of the principal factors that determine the quality of available optical observing time. At any site the optical night sky is always brightened with airglow, zodiacal light, integrated starlight, diffuse Galactic light and extra-galactic light. Further brightening can be caused by scattered sunlight, aurorae, moonlight and artificial sources. Dome C exhibits many characteristics that are extremely favourable to optical and IR astronomy; however, at this stage few measurements have been made of the brightness of the optical night sky. Nigel is a fibre-fed UV/visible grating spectrograph with a thermoelectrically cooled 256 x 1024 pixel CCD camera, and is designed to measure the twilight and night sky brightness at Dome C from 250 nm to 900 nm. We present details of the design, calibration and installation of Nigel in the AASTINO laboratory at Dome C, together with a summary of the known properties of the Dome C sky.