We introduce LEGUS, a Hubble Space Telescope program which will provide a critical missing piece in our efforts to solve the star formation puzzle: a robust characterization of the links between star formation on two fundamental scales, those of individual young stars, stellar clusters and associations over parsec scales, and of galaxy disks over kiloparsec scales. As a 154-orbit Treasury survey, LEGUS has begun obtaining NUV,U,B,V,I imaging of 50 star-forming galaxies, at distances of 4-12 Mpc. The dataset is guaranteed to have exceptional legacy value, as the targets have been carefully selected to uniformly sample a full range of global galaxy properties, as well as have the largest suites of multi-wavelength ancillary data available. The high-resolution HST NUV and U imaging are key for deriving accurate recent (<50 Myr) star formation histories from resolved massive stars, along with the ages and masses for complete samples of star clusters and associations in each galaxy. We present an overview of the sample, the observations, and provide a first look at the science that the LEGUS team is pursuing. A companion poster presents the status of the program, and a more detailed description of the extensive data products being developed which will seed community science, and provide a foundation for studies of star formation with ALMA and JWST.