  A liquid helium target system was designed and built to perform a precision
measurement of the parity-violating neutron spin rotation in helium due to the
nucleon-nucleon weak interaction. The measurement employed a beam of low energy
neutrons that passed through a crossed neutron polarizer--analyzer pair with
the liquid helium target system located between them. Changes between the
target states generated differences in the beam transmission through the
polarizer--analyzer pair. The amount of parity-violating spin rotation was
determined from the measured beam transmission asymmetries. The expected
parity-violating spin rotation of order $10^{-6}$ rad placed severe constraints
on the target design. In particular, isolation of the parity-odd component of
the spin rotation from a much larger background rotation caused by magnetic
fields required that a nonmagnetic cryostat and target system be supported
inside the magnetic shielding, while allowing nonmagnetic motion of liquid
helium between separated target chambers. This paper provides a detailed
description of the design, function, and performance of the liquid helium
target system.
