  We describe atoms by a pseudo-relativistic model that has its origin in the
work of Chandrasekhar. We prove that the leading energy correction for heavy
atoms, the Scott correction, exists. It turns out to be lower than in the
non-relativistic description of atoms. Our proof is valid up to and including
the critical coupling constant. It is based on a renormalization of the energy
whose zero level we adjust to be the ground-state energy of the corresponding
non-relativistic problem. This allows us to roll the proof back -- by
relatively simple technical means -- to results for the Schr\"odinger operator.
