Samples that have been etched to reveal fossil fission tracks contain an accompanying high density of shallow etch pits that are clearly visible using phase contrast optical microscopy. A number of lines of evidence demonstrates conclusively that these shallow pits are produced by the heavy recoil nuclei accompanying alpha-decay of U and Th impurities. Measurement of the density of fossil alpha-recoil tracks, coupled with measures of the track densities induced by separate slow and fast neutron irradiations, gives a new track dating method. The new method is somewhat more complicated than the previously discovered fission track method, but is some 3,000 times more sensitive. Because of this enhanced sensitivity, the alpha-recoil method of dating has a number of potential interesting applications. It should prove particularly useful in connection with the problem of extinct isotopes in meteorites.