Criegee intermediates (CIs) are a class of reactive radicals that are thought to play a key role in atmospheric chemistry through reactions with trace species that can lead to aerosol particle formation. Recent work has suggested that water vapor is likely to be the dominant sink for some CIs, although reactions with trace species that are sufficiently rapid can be locally competitive. Herein, we use broadband transient absorption spectroscopy to measure rate constants for the reactions of the simplest CI, CH2OO, with two inorganic acids, HCl and HNO3, both of which are present in polluted urban atmospheres. Both reactions are fast; at 295 K, the reactions of CH2OO with HCl and HNO3 have rate constants of 4.6×10−11 cm3 s−1 and 5.4×10−10 cm3 s−1, respectively. Complementary quantum‐chemical calculations show that these reactions form substituted hydroperoxides with no energy barrier. The results suggest that reactions of CIs with HNO3 in particular are likely to be competitive with those with water vapor in polluted urban areas under conditions of modest relative humidity.