For a spatially homogeneous gas a kinetic equation is obtained in the approximation of triple collisions. It differs from the well-known Choh–Uhlenbeck equation by the more complete allowance for triple collisions in the nondissipative characteristics of the gas. From the kinetic equation we obtain in particular the energy conservation law, in which the internal energy contains the first three terms of the virial expansion. The Choh–Uhlenbeck equation yields only the first two terms of the virial expansion, so that the contribution of triple collisions is not allowed for completely. In the derivation of the kinetic equation only the principal terms are allowed for in the distribution function of four particles when the chain of equations is decoupled. This is sufficient to obtain a kinetic equation with the above properties.