  Observations of the optical polarization of NGC 4151 in 1997-2003 show
variations of an order of magnitude in the polarized flux while the
polarization position angle remains constant. The amplitude of variability of
the polarized flux is comparable to the amplitude of variability of the total
U-band flux, except that the polarized flux follows the total flux with a lag
of 8 +/- 3 days. The time lag and the constancy of the position angle strongly
favor a scattering origin for the variable polarization rather than a
non-thermal synchrotron origin. The orientation of the position angle of the
polarized flux (parallel to the radio axis) and the size of the lag imply that
the polarization arises from electron scattering in a flattened region within
the low-ionization component of the broad-line-region. Polarization from dust
scattering in the equatorial torus is ruled out as the source of the lag in
polarized flux because it would produce a larger lag and, unless the
half-opening angle of the torus is more than 53 degrees, the polarization would
be perpendicular to the radio axis. We note a long-term change in the
percentage of polarization at similar total flux levels and this could be due
either to changing non-axisymmetry in the optical continuum emission, or a
change in the number of scatterers on a timescale of years.
