Concentration gradients in glass adjacent to skeletal olivines in a DSDP basalt have been examined by electron probe. The glass is depleted in Mg, Fe, and Cr and enriched in Si, Al, Na, and Ca relative to that far from olivine. Ionic diffusion coefficients for the glass compositions are calculated from temperature, ionic radius and melt viscosity, using the Stokes-Einstein relation. At 1170 degrees C, the diffusion coefficient of Mg2+ ions in the basalt is 4-5-10-9 cm (super 2) /s. Comparison with measured diffusion coefficients in a mugearite suggests this value may be 16 times too small. The concentration gradient data and the diffusion coefficients are used to calculate instantaneous olivine growth rates of 2-6-10-7 cm/s. This is too slow for olivine to have grown in situ during quenching. Growth necessarily preceded emplacement such that the composition of the crystals plus the enclosing glass need not be that of a melt. The computed olivine growth rates are compatible with the rate of crystallization deduced for the Skaegaard intrusion.