A pair of samples, from host lava and an included segregation vein from the Reykjanes Peninsula, Iceland, allows the assessment of a complete fractional crystallization of an olivine tholeiite at low pressure. The final product consists of silicic glasses with bimodal composition: trondhjemitic and more rarely granitic. Compilation of data on major element compositions of Icelandic silicic rocks reveals a clear difference from those of the segregation glasses. Fractional crystallization of basalts at low pressure is therefore not the most likely mechanism for the origin of silicic magmas in Iceland. Similar conclusions have been reached in studies on O- and Th-isotope compositions. On the other hand, the trondhjemitic compositions of the glasses in the segregation vein from Reykjanes Peninsula suggest that fractional crystallization of olivine tholeiites could have played a significant role during the formation of the very early continental crust.