  We report measurements of the specific heat and the thermal conductivity of
the model Heisenberg spin-1/2 chain cuprate Sr$_{2}$CuO$_{3}$ at low
temperatures. In addition to a nearly isotropic phonon heat transport, we find
a quasi one-dimensional excess thermal conductivity along the chain direction,
most likely associated with spin excitations (spinons). The spinon energy
current is limited mainly by scattering on defects and phonons. Analyzing the
specific heat data, the intrachain magnetic exchange $J/k_{B}$ is estimated to
be 2650 K.
