Measurements of solar ultraviolet irradiance obtained by a Brewer spectrophotometer located in Chicago, Illinois, reveal a wavelength-dependent excess attenuation associated with cloudy skies beyond that expected from the column ozone amount. When each observation is expressed as a fraction of the irradiance that would have existed under clear skies, a quantity called the transmission ratio, values for a wavelength band near 305 nm are generally smaller than those for a band near 345 nm under dense cloud cover. Transmission ratios computed for wavelength bands near 310 nm and 315 nm lie in between those for the above wavelengths. The observations are consistent with absorption of radiation in the interstitial air of a cloud, while the magnitude and wavelength dependence are like those expected from ozone. A radiative transfer calculation shows that ozone amounts typical of the troposphere are accompanied by enhanced absorption when placed in a medium that is optically thick in scattering. This mechanism constitutes a coupling between tropospheric air quality and the attenuation of sunlight provided by cloudy skies in the chemically active ultraviolet portion of the spectrum.