The tunnelling of electrons through molecules (and through any nanoscale insulating and dielectric material(1)) shows exponential attenuation with increasing length(2), a length dependence that is reflected in the ability of the electrons to carry an electrical current. It was recently demonstrated(3-5) that coherent tunnelling through a molecular junction can also be suppressed by destructive quantum interference(6), a mechanism that is not length-dependent. For the carbon-based molecules studied previously, cancelling all transmission channels would involve the suppression of contributions to the current from both the pi-orbital and sigma-orbital systems. Previous reports of destructive interference have demonstrated a decrease in transmission only through the pi-channel. Here we report a saturated silicon-based molecule with a functionalized bicyclo [2.2.2] octasilane moiety that exhibits destructive quantum interference in its sigma-system. Although molecular silicon typically forms conducting wires, we use a combination of conductance measurements and ab initio calculations to show that destructive sigma-interference, achieved here by locking the silicon-silicon bonds into eclipsed conformations within a bicyclic molecular framework, can yield extremely insulating molecules less than a nanometre in length. Our molecules also exhibit an unusually high thermopower (0.97 millivolts per kelvin), which is a further experimental signature of the suppression of all tunnelling paths by destructive interference: calculations indicate that the central bicyclo[2.2.2]octasilane unit is rendered less conductive than the empty space it occupies. The molecular design presented here provides a proof-of-concept for a quantum-interference-based approach to single-molecule insulators.