We present a study of the magnetic field-dependent thermal transport in the spin S=1 chain material Ni(C(2)H(8)N(2))(2)NO(2)(ClO(4)) (NENP). The measured thermal conductivity is found to be very sensitive to the field-induced changes in the spin excitation spectrum. The magnetic contribution to the total heat conductivity is analyzed in terms of a quasiparticle model, and we obtain a temperature and momentum independent mean free path. This implies that the motion of quasiparticles is effectively three dimensional despite the tiny interchain coupling.