  In this paper we construct a string-like classical solution, the pion-string,
in the linear sigma model. We then study the stability of the pion-string, and
find that it is unstable in the parameter space allowed experimentally. We also
speculate on the existance of an unstable eta-string, associated with
spontaneous breakdown of the anomalous $U_A(1)$ symmetry in QCD at high
temperatures. The implications of the pion and eta strings for cosmology and
heavy ion collisions are briefly mentioned.
