The CHaracterizing ExOPlanet Satellite (CHEOPS) will be the first mission dedicated to search for transits by means of ultrahigh precision photometry on bright stars already known to host planets. By being able to point at nearly any location on the sky, it will provide the unique capability of determining accurate radii for a subset of those planets for which the mass has already been estimated from ground-based spectroscopic surveys. It will also provide precision radii for new planets discovered by the next generation ground-based transits surveys (Neptune-size and smaller). Large ground-based high-precision Doppler spectroscopic surveys carried out during the last years have identified hundreds of stars hosting planets in the super-Earth to Neptune mass range (1<Mplanet/MEarth<20) and will continue to do so into the foreseeable future. The characteristics of these stars (brightness, low activity levels, etc.) and the knowledge of the planet ephemerids make them ideal targets for precision photometric measurements from space. CHEOPS will be the only facility able to follow-up all these targets for precise radius measurements. The new generation of ground-based transit surveys (e.g. NGTS), capable of reaching 1 mmag precision on V < 13 magnitude stars, provide yet another source of targets. By the end of 2017, NGTS will provide of order 50 targets with R < 6 REarth for which CHEOPS will be able to measure radii to a precision of 10%. These stars are also bright enough for precise radial velocity follow-up measurements to be practical. While unbiased ground-based searches are well-suited to detect the transits and fix the ephemerids, CHEOPS is crucial to obtain precise measurements of planet radii.