We present the design of, and the science drivers for, the Visible Integral-field Replicable Unit Spectrograph (VIRUS). This instrument is made up of 145 individually small and simple spectrographs, each fed by a fiber integral field unit. The total VIRUS-145 instrument covers ~30 sq. arcminutes per observation, providing integral field spectroscopy from 340 to 570 nm, simultaneously, of 35,670 spatial elements, each 1 sq. arcsecond on the sky. This corresponds to 15 million resolution elements per exposure. VIRUS-145 will be mounted on the Hobby-Eberly Telescope and fed by a new wide-field corrector with 22 arcminutes diameter field of view. VIRUS represents a new approach to spectrograph design, offering the science multiplex advantage of huge sky coverage for an integral field spectrograph, coupled with the engineering multiplex advantage of >100 spectrographs making up a whole. VIRUS is designed for the Hobby-Eberly Telescope Dark Energy Experiment (HETDEX) which will use baryonic acoustic oscillations imprinted on the large-scale distribution of Lyman-α emitting galaxies to provide unique constraints on the expansion history of the universe that can constrain the properties of dark energy.