Urban O3 is produced by photochemical chain reactions that amplify background O3 in mixtures of gaseous nitrogen oxides (NOx) and organic molecules. Current thinking treats NOx and organics as independent variables that limit O3 production depending on the NOx to organic ratio; in this paradigm, reducing organics either has no effect or reduces O3. We describe a theoretical counterexample where NOx and organics are strongly coupled and reducing organics increases O3 production, and illustrate the example with observations from Mexico City. This effect arises from chain termination in the HOx and NOx cycles via organic nitrate production. We show that reductions in VOC reactivity that inadvertently reduce organic nitrate production rates will be counterproductive without concurrent reductions in NOx or other organics.