The kinetic foundations of Tsallis' nonextensive thermostatistics are
investigated through Boltzmann's transport equation approach. Our analysis
follows from a nonextensive generalization of the ``molecular chaos
hypothesis". For q>0, the q-transport equation satisfies an H-theorem
based on Tsallis entropy. It is also proved that the collisional equilibrium is
given by Tsallis' q-nonextensive velocity distribution.Comment: 4 pages, no figures, corrected some typo