We consider the KdV equation used for modeling, e.g., water waves in a narrow channel. The time evolution is described by a quadratic (Burgers') plus a linear (Airy) term. Since the evolution of each of these terms is quite different, it is natural to ask whether the concatenation of the evolution operators for each term yields an approximation to the evolution operator for the sum. This strategy has been used with good results when designing numerical methods for the KdV equation, but without rigourous convergence proofs. The aim of this talk is to present a first step in this direction, and show convergence of operator splitting for sufficiently regular initial data. (Joint work with N. H. Risebro, K. H. Karlsen, T. Tao.)