This paper deals with the Boltzmann billiard , that is, a billiard subjected to a central force of the type V(r)=-\alpha/r-\beta/r^{2} , \alpha and \beta being real constants, and with a straight reflection table. In the particular case of \alpha and \beta positive, we prove the presence of a symbolic dynamics, and hence of positive topological entropy, at positive energy for \beta sufficiently small.