It is pointed out that isotope fractionation as a result of chemical reactions is due to the small zero-point energy differences between reactants and products of isotopically distinct species. Only at temperatures near absolute zero does this energy difference become significant. Favorable conditions for isotope fractionation on the considered basis exist in space within dense interstellar clouds. Temperatures of approximately 10 K may occur in these clouds. Under such conditions, ion-molecule reactions have the potential to distribute isotopes of hydrogen, carbon, oxygen unequally among the interstellar molecules. The present investigation makes use of a detailed model of the time-dependent chemistry of dense interstellar clouds to study cosmological isotope fractionation. Attention is given to fractionation chemistry and the calculation of rate parameters, the isotope fractionation results, and a comparison of theoretical results with observational data.