It is well known that, when working in the harmonic approximation, the contribution of the lattice vibrations to the specific heat of solids approaches the Dulong‐Petit value at high temperatures. Experimentally, considerable deviations from the Dulong‐Petit value have been observed in certain materials. One question that arises in this connection is: Can anharmonic forces account for the observed differences? The answer to this question depends on the lattice spacing as well as on the harmonic and anharmonic force constants. For reasonable values of these parameters, our work seems to imply that if one demands that the rms amplitude of vibration of the atom be less than approximately one‐half the lattice spacing, then ``large'' deviations from the Dulong‐Petit value are not to be expected. The model we use is that of a linear chain with harmonic and anharmonic forces between nearest neighbors.