In this paper, we propose to combine two promising research topics in accelerator physics, i.e., optical stochastic cooling (OSC) and steady-state microbunching (SSMB). Our study shows that such an OSC-SSMB storage ring with a circumference of 50 m and beam energy of several hundred MeVs using present technology can deliver kilowatt radiation at 100 nm wavelength. A more ambitious application of OSC in an SSMB ring can push the radiation wavelength to an even shorter wavelength, such as EUV and soft X-ray. Such a powerful compact light source could benefit fundamental science research and industry applications.