  We investigate the energy transport in a one-dimensional lattice of
oscillators with a harmonic nearest neighbor coupling and a harmonic plus
quartic on-site potential. As numerically observed for particular coupling
parameters before, and confirmed by our study, such chains satisfy Fourier's
law: a chain of length N coupled to thermal reservoirs at both ends has an
average steady state energy current proportional to 1/N. On the theoretical
level we employ the Peierls transport equation for phonons and note that beyond
a mere exchange of labels it admits nondegenerate phonon collisions. These
collisions are responsible for a finite heat conductivity. The predictions of
kinetic theory are compared with molecular dynamics simulations. In the range
of weak anharmonicity, respectively low temperatures, reasonable agreement is
observed.
