A ground-based search for stratospheric chlorine monoxide was carried out during May and October 1981 with an infrared heterodyne spectrometer in the solar absorption mode. Lines due to stratospheric nitric acid and tropospheric carbonyl sulfide were detected at about 0.2 percent absorptance levels, but the expected 0.1 percent lines of chlorine monoxide in this same region were not seen. Stratospheric chlorine monoxide is less abundant by at least a factor of 7 than is indicated by in situ measurements, and the upper limit for the integrated vertical column density of chlorine monoxide is 2.3 x 10(13) molecules per square centimeter at the 95 percent confidence level. These results imply that the release of chlorofluorocarbons may be significantly less important for the destruction of stratospheric ozone than is currently thought.