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CK Vulpeculae, which erupted in AD 1670-71, was long considered to be a nova outburst; however, recent observations have required that alternative scenarios be considered. Long slit infrared spectroscopy of a forbidden line of iron reported here has revealed high line-of-sight velocities ($\sim\pm900$~km~s$^{-1}$) of the ansae at the tips of the bipolar lobes imaged in H$α$ in 2010. The deprojected velocities of the tips are approximately $\pm2130$~km~s$^{-1}$ assuming the previously derived inclination angle of $65^\circ$ for the axis of cylindrical symmetry of the bipolar nebula. Such high velocities are in stark contrast to previous reports of much lower expansion velocities in CK~Vul. Based on the deprojected velocities of the tips and their angular expansion measured over a 10-year baseline, we derive a revised estimate, with estimated uncertainties, of $3.2^{+0.9}_{-0.6}$~kpc for the distance to CK~Vul. This implies that the absolute visual magnitude at the peak of the 1670 explosion was $M_V = -12.4^{+1.3}_{-2.4}$, indicating that the 1670 event was far more luminous than previous estimates and brighter than any classical nova or any Galactic stellar merger. We propose that CK~Vul belongs to the class of Intermediate Luminosity Optical Transients (ILOTs), objects which bridge the luminosity gap between novae and supernovae. While eruptions in lower luminosity ILOTs are attributed to merger events, the origin of the highly luminous ILOT outbursts is currently not known.