The gas permeability of poly[ 1-(trimethylsilyl)-1-propynel (PTMSP) containing nanoparticulate fumed silica increases with increasing filler content. This unusual phenomenon is explored using Xe-129 NMR spectroscopy to examine the effect of filler on the free volume of the PTMSP host matrix. The Xe-129 NMR chemical shift decreases regularly with increasing fumed silica concentration, consistent with an increase in the average size of free volume elements or cavities through which molecular transport can occur. A relationship between the chemical shift and gas permeability in the filled polymer is reported.