The conventional radiocarbon dating method relies on the accurate measurement of a sample's beta-ray decay rate in order to determine the age of the sample. The new method instead counts the individual C14 atoms in a sample using an ultra-sensitive mass spectrometer. There are numerous advantages to this approach. The problem of cosmic ray background does not arise. Shorter counting times on samples a thousand times smaller may be possible. We might also expect the production of more accurate age determinations. The new method will permit a great expansion in the variety of archaeological materials which can be dated because only milligram samples will be required. Research on the design of a dedicated C14 atom-counting machine is now in progress. This note is by E. B. Banning, Department of Near Eastern Studies and Department of Physics Archaeometry Laboratory, University of Toronto, Canada, and L. A. Pavlish, Department of Anthropology and Department of Physics Archaeometry Laboratory, University of Toronto, Canada.