  Motivated by the desire to understand chaos in the $S$-matrix of string
theory, we study tree level scattering amplitudes involving highly excited
strings. While the amplitudes for scattering of light strings have been a
hallmark of string theory since its early days, scattering of excited strings
has been far less studied. Recent results on black hole chaos, combined with
the correspondence principle between black holes and strings, suggest that the
amplitudes have a rich structure. We review the procedure by which an excited
string is formed by repeatedly scattering photons off of an initial tachyon
(the DDF formalism). We compute the scattering amplitude of one arbitrary
excited string and any number of tachyons in bosonic string theory. At high
energies and high mass excited state these amplitudes are determined by a
saddle-point in the integration over the positions of the string vertex
operators on the sphere (or the upper half plane), thus yielding a
generalization of the "scattering equations". We find a compact expression for
the amplitude of an excited string decaying into two tachyons, and study its
properties for a generic excited string. We find the amplitude is highly
erratic as a function of both the precise excited string state and of the
tachyon scattering angle relative to its polarization, a sign of chaos.
