  We present deep optical observations of the gravitational lens system CLASS
B0218+357, from which we derive an estimate of the Hubble constant. Extensive
radio observations have reduced the degeneracies between Hubble's constant and
the mass model in this lens to one involving only the position of the
radio-quiet lensing galaxy relative to the lensed images. B0218+357 has an
image separation of only 334 mas, so optical observations have previously been
unable to resolve the lens galaxy from the bright lensed images. Using the new
Advanced Camera for Surveys installed on the Hubble Space Telescope, we have
measured the separation between the lens galaxy centre and the brightest image.
The position found, and hence our estimate of Hubble's constant, depends on our
approach to the spiral arms in B0218+357. If the most prominent arms are left
unmasked, we find a value for Hubble's constant of 70+/-5 km/s /Mpc (95%
confidence). If the spiral arms are masked out, we find a value of 61+/-7 km/s
/Mpc (95% confidence).
