We investigate the possibility of fermion confinement in a manifestly chiral-invariant theory. In particular we study the nonlinear σ model in one time and one space dimension, and demonstrate that it is equivalent to the massive Thirring model plus a free massless scalar field. We find an exact, time-independent, classical solution to the massive Thirring model. This solution is characterized by a fermion confined in a self-generated potential. In the σ-model analog of this solution, the chiral phase changes rapidly in the region of the confined fermion, and has two different constant limits on either side of this region. We also consider the case in which the mass of the pseudoscalar meson is small but finite, and find an approximate solution which displays both partial conservation of axial-vector current and fermion confinement.