  We have measured the thermal conductivity along the c-axis, \k{appa}||c,
parallel to ferromagnetic spin-chains of single crystals of the S = 1/2
quasi-one-dimensional spin system CsCuCl3 in magnetic fields up to 14 T, in
order to investigate the thermal conductivity due to spins, \k{appa}spin, and
the change of thermal conductivity corresponding to the change of the spin
state. In the temperature dependence of \k{appa}||c, no contribution of
\k{appa}spin has been observed, while a dip has been observed at the
antiferromagnetic phase transition temperature, TN. Furthermore, it has been
found that \k{appa}||c at a low temperature of 5.1 K below TN changes with
increasing field perpendicular to the c-axis in good correspondence to the
field-induced change of the spin state.
