We report the detection of the secondary eclipse of the hot Jupiter HD 209458 b in optical/visible light using the CHEOPS space telescope. Our measurement of 20.4 −3.3 +3.2 parts per million translates into a geometric albedo of A g  = 0.096 ± 0.016. The previously estimated dayside temperature of about 1500 K implies that our geometric albedo measurement consists predominantly of reflected starlight and is largely uncontaminated by thermal emission. This makes the present result one of the most robust measurements of A g for any exoplanet. Our calculations of the bandpass-integrated geometric albedo demonstrate that the measured value of A g is consistent with a cloud-free atmosphere, where starlight is reflected via Rayleigh scattering by hydrogen molecules, and the water and sodium abundances are consistent with stellar metallicity. We predict that the bandpass-integrated TESS geometric albedo is too faint to detect and that a phase curve of HD 209458 b observed by CHEOPS would have a distinct shape associated with Rayleigh scattering if the atmosphere is indeed cloud free.