  Using the fact the BTZ black hole is a quotient of AdS_3 we show that
classical string propagation in the BTZ background is integrable. We construct
the flat connection and its monodromy matrix which generates the non-local
charges. From examining the general behaviour of the eigen values of the
monodromy matrix we determine the set of integral equations which constrain
them. These equations imply that each classical solution is characterized by a
density function in the complex plane. For classical solutions which correspond
to geodesics and winding strings we solve for the eigen values of the monodromy
matrix explicitly and show that geodesics correspond to zero density in the
complex plane. We solve the integral equations for BMN and magnon like
solutions and obtain their dispersion relation. Finally we show that the set of
integral equations which constrain the eigen values of the monodromy matrix can
be identified with the continuum limit of the Bethe equations of a twisted
SL(2, R) spin chain at one loop.
