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.Facultad de Ciencias Astronómicas y Geofísicas