  We report the first extensive set of optical photometric observations of the
counterpart to SAX J1808.4-3658 (V4580 Sagittarius) in quiescence. The source
was detected at V~21, 5 magnitudes fainter than at the peak of its 1998
outburst. However, a comparable ~6% semi-amplitude 2hr modulation of its flux
is revealed. This has the same phasing and approximately sinusoidal modulation
as seen during outburst and with photometric minimum when the pulsar is behind
the companion. The lack of a double-humped morphology rules out an ellipsoidal
origin, implying that the bulk of the optical flux does not arise from the
companion. Moreover, applying crude modelling to the disc and X-ray irradiated
face of the donor shows that the internal energy release of a remnant disc
(with mass transfer driven by gravitational radiation) is sufficient to explain
most of the optical emission, and with the modulation due to the varying
contribution of the heated star's face. We note that this model is also
consistent with the much lower X-ray to optical flux ratio in quiescence versus
outburst, and with the phasing of the optical modulation.
