We report the discovery of trailing grand-design nuclear spiral structure in the spiral galaxy NGC 5248. Two tightly wound red spiral arms, with widths less than 1 arcsec (~ 75 pc), emanate at 1 arcsec outside the quiescent nucleus of the galaxy, and can be followed for 3 arcsec, appearing to end before the radius of the circumnuclear starburst `ring', which is at 5--6 arcsec or around 400 pc. Combining our near-infrared Canada--France--Hawaii Telescope adaptive optics results with traditional near-infrared and optical imaging, we show that spiral structure is present in this galaxy at spatial scales covering two orders of magnitude, from 100 pc to 15 kpc. Comparison with a Hubble Space Telescope ultraviolet image shows how the location of the circumnuclear star formation relates to the nuclear spiral structure. We briefly discuss possible mechanisms that could be responsible for the observed nuclear grand-design spiral structure.