We present the computer simulation results of a chain of hard-point particl
es with alternating masses interacting on its extremes with two thermal bat
hs at different temperatures. We found that the system obeys Fourier's law
at the thermodynamic limit. This result is against the actual belief that o
ne-dimensional systems with momentum conservative dynamics and nonzero pres
sure have infinite thermal conductivity. It seems that thermal resistivity
occurs in our system due to a cooperative behavior in which light particles
tend to absorb much mure energy than the heavier ones.