  We report a study of the low-temperature thermal conductivity of
NiCl_{2}-4SC(NH_{2})_{2}, which is a spin-1 chain system exhibiting the magnon
Bose-Einstein condensation (BEC) in magnetic field. It is found that the low-T
thermal conductivity along the spin-chain direction shows strong anomalies at
the lower and upper critical fields of the magnon BEC state. In this state,
magnons act mainly as phonon scatterers at relatively high temperature, but
change their role to heat carriers upon temperature approaching zero. The
result demonstrates a large thermal conductivity in the magnon BEC state and
points to a direct analog between the magnon BEC and the conventional one.
