Quasars are the most luminous of active galactic nuclei, and are perhaps responsible for quenching star formation in their hosts. We have 2500 X-ray detected sources in the Stripe 82 field with multi-wavelength counterparts, and 30% of these are unobscured quasars. We define a new population of quasars which are unobscured, have X-ray luminosities in excess of 1044erg/s, have broad emission lines, and yet are also bright in the far-infrared, with a 250μm flux density of S250>30mJy. We refer to these Herschel-detected, unobscured quasars as “Cold Quasars”. A mere 4% (21) of the X-ray- and optically-selected unobscured quasars in Stripe 82X are detected at 250μm. These Cold Quasars lie at z=1−3, have LIR>1012L⊙, and have star formation rates of 200−1400M⊙/yr. Cold Quasars are bluer in the mid-IR than the full quasar population. Crucially, Cold Quasars have on average 9× as much star formation as the main sequence of star forming galaxies at similar redshifts. Although dust-rich, unobscured quasars have occasionally been noted in the literature before, we argue that they should be considered as a separate class of quasars due to their high star formation rates. This phase is likely short-lived, as the central engine and immense star formation consume the gas reservoir. Cold Quasars are Type-1 blue quasars that reside in starburst galaxies.