  Gott spacetime has closed timelike curves, but no locally anomalous
stress-energy. A complete orthonormal set of eigenfunctions of the wave
operator is found in the special case of a spacetime in which the total deficit
angle is $2\pi$. A scalar quantum field theory is constructed using these
eigenfunctions. The resultant interacting quantum field theory is not unitary
because the field operators can create real, on-shell, particles in the acausal
region. These particles propagate for finite proper time accumulating an
arbitrary phase before being annihilated at the same spacetime point as that at
which they were created. As a result, the effective potential within the
acausal region is complex, and probability is not conserved. The stress tensor
of the scalar field is evaluated in the neighborhood of the Cauchy horizon; in
the case of a sufficiently small Compton wavelength of the field, the stress
tensor is regular and cannot prevent the formation of the Cauchy horizon.
