We present a deep image of the optically powerful quasar E1821+643 at 18 cm made with the Very Large Array. This image reveals radio emission, over 280 h(-1) kpc in extent, elongated way beyond the quasar's host galaxy. Its radio structure has decreasing surface brightness with increasing distance from the bright core, characteristic of FR I sources. Its radio luminosity at 5 GHz falls in the classification for "radio-quiet" quasars (it is only 10(23.9) W Hz(-1) sr(-1)). Its radio luminosity at 151 MHz (which is 10(25.3) W Hz(-1) sr(-1)) is at the transition luminosity observed to separate FR I and FR II structures. Hitherto, no optically powerful quasar had been found to have a conventional FR I radio structure. For searches at low frequency, this is unsurprising given current sensitivity and plausible radio spectral indices for radio-quiet quasars. We demonstrate the inevitability of the extent of any FR I radio structures being seriously underestimated by existing targeted follow-up observations of other optically selected quasars, which are typically short exposures of objects, and we discuss the z > 0.3 implications for the purported radio bimodality in quasars. The nature of the inner arcsecond-scale jet in E1821+643, together with its large-scale radio structure, suggest that the jet axis in this quasar is precessing (cf. Galactic jet sources such as SS 433). A possible explanation for this is that its central engine is a binary whose black holes have yet to coalesce. The ubiquity of precession in radio-quiet quasars, perhaps as a means of reducing the observable radio luminosity expected in highly accreting systems, remains to be established.