The lump-of-labor fallacy has been called one of the “best known fallacies in economics.” It is widely cited in disparagement of policies for reducing the standard hours of work, yet the authenticity of the fallacy claim is questionable, and explanations of it are inconsistent and contradictory. This article discusses recent occurrences of the fallacy claim and investigates anomalies in the claim and its history. S.J. Chapman's coherent and formerly highly regarded theory of the hours of labor is reviewed, and it is shown how that theory could lend credence to the job-creating potentiality of shorter working time policies. It concludes that substituting a dubious fallacy claim for an authentic economic theory may have obstructed fruitful dialogue about working time and the appropriate policies for regulating it.