  We report a significant detection of weak, tangential distortion of the
images of cosmologically distant, faint galaxies due to gravitational lensing
by foreground galaxies. A mean image polarisation of $<p>=0.011\pm 0.006$ is
measured for 3202 pairs of source galaxies with magnitudes $23< r \le 24$ and
lens galaxies with magnitudes $20\le r\le 23$. The signal remains strong for
lens-source separations $\lo 90''$, consistent with quasi-isothermal galaxy
halos extending to large radii ($\go 100h^{-1}$ kpc). Our observations thus
provide the first evidence from weak gravitational lensing of large scale dark
halos associated with individual galaxies. The observed polarisation is also
consistent with the signal expected on the basis of simulations incorporating
measured properties of local galaxies and modest extrapolations of the observed
redshift distribution of faint galaxies. From the simulations we derive a
best-fit halo circular velocity of $V\sim 220$ km/s and characteristic radial
extent of $s \go 100h^{-1}$ kpc. Our best-fit halo parameters imply typical
masses for the lens galaxies within a radius of $100h^{-1}$ kpc on the order of
$1.0^{+1.1}_{-0.7}\times 10^{12}h^{-1} M_\odot$, in good agreement with recent
dynamical estimates of the masses of local spiral galaxies. This is
particularly encouraging as the lensing and dynamical mass estimators rely on
different sets of assumptions. Contamination of the gravitational lensing
signal by a population of tidally distorted satellite galaxies can be ruled out
with reasonable confidence. The prospects for corroborating and improving this
measurement seem good, especially using deep HST archival data.
