  Deep Very Large Array imaging of the quasar 3C\,345 at 4.86 and 8.44 GHz has
been used to study the structure and linear polarization of its radio jet on
scales ranging from 2 to 30 kpc. There is a 7--8 Jy unresolved core with
spectral index $\alpha \simeq -0.24$ ($I_\nu \propto \nu^{\alpha}$). The jet
(typical intensity 15 mJy/beam) consists of a $2.5\arcsec$ straight section
containing two knots, and two additional non-co-linear knots at the end. The
jet's total projected length is about 27 kpc. The spectral index of the jet
varies over $-1.1 \lesssim \alpha \lesssim -0.5$. The jet diverges with a
semi-opening angle of about $9^\circ$, and is nearly constant in integrated
brightness over its length. A faint feature north-east of the core does not
appear to be a true counter-jet, but rather an extended lobe of this FR-II
radio source seen in projection. The absence of a counter-jet is sufficient to
place modest constraints on the speed of the jet on these scales, requiring
$\beta \ga 0.5$. Despite the indication of jet precession in the total
intensity structure, the polarization images suggest instead a jet re-directed
at least twice by collisions with the external medium.
  Surprisingly, the electric vector position angles in the main body of the jet
are neither longitudinal nor transverse, but make an angle of about $55^\circ$
with the jet axis in the middle while along the edges the vectors are
transverse, suggesting a helical magnetic field. There is no significant
Faraday rotation in the source, so that is not the cause of the twist. The
fractional polarization in the jet averages 25% and is higher at the edges. In
a companion paper it is shown that differential Doppler boosting in a diverging
relativisitic velocity field can explain the electric vector pattern in the
jet.
