An analytic study of horseshoe chaos in a plane conservative system with a cubic potential is presented. It is shown that this problem with two degrees of freedom can be reduced to a time-periodically perturbed Hamiltonian system with just one degree of freedom. The unperturbed reduced system exhibits homoclinic paths, and the main goal of our study is the investigation of their break-up. The determination of the Melnikov function shows that there is no contribution from two of the four cubic potential terms. The locus of homoclinic bifurcation in a parameter plane is computed and this bifurcation can be interpreted in terms of energy arguments. It was found that an increase of the total energy leads - independent of the particular parameter combination - from non-chaotic to chaotic motion.