A filament-stretching rheometer is used to measure the extensional properties of shear-thickening nanoparticle suspensions as a function of concentration and extension rate. The experiments are performed using a series of colloidal suspensions consisting of concentrations of 17.5 wt%, 25 wt% and 30 wt% of fumed silica nanoparticles in polypropylene glycol. The shear rheology of these suspensions was found to demonstrate dynamic shear-thickening behavior owing to the formation of large hydrodynamic clusters. The critical value of angular frequency for the onset of shear-thickening was found to increase monotonically with decreased strain amplitude. The extensional rheology of all the tested suspensions demonstrated modest strain-hardening at low strain rates. At a critical extension rate, a dramatic increase in both the speed and magnitude of the strain-hardening is observed for both the 25 wt% and 30 wt% suspensions with increasing extensional rate. The steady state extensional viscosity as a function of extension rate shows sharp extensional thickening transition very similar to shear flows. The increase in strain-hardening is likely due to the formation of strings and clusters ordered in the flow direction. This hypothesis is confirmed by small-angle light scattering measurements of the flow of the nanoparticle suspension through a microfluidic hyperbolic contraction. The degree of alignment of nanoparticles is quantified from the analysis of the scattering patterns and found to increase significantly with increasing extension rate.