Significant nanoporosity as indicated by positron annihilation lifetime spectroscopy (PALS) has been observed in a metakaolin-based geopolymer. The nanoporosity was indicated by a component of the PALS spectrum having a lifetime of 1.5-2 ns, characterizing a pore diameter size of similar to 0.5 nm. Progressive heating to 600 degrees C decreased the intensity of this spectral component from similar to 10% to 2.5%. Positron annihilation in free pore water appears to be only a minor contributor to this spectral component. The Barrett-Joyner-Halenda (BJH) method pore distribution data, derived from BET nitrogen adsorption isotherms, showed the presence of considerable meso- and macroporosity in the samples. However, these porosities were not evident in the PALS spectrum. Heating from 150 degrees to 600 degrees C progressively changed the smallest detectable pore size via the BJH method from 3.3 to 7.1 nm.