We introduce the KWIK algorithm for computing the Coulomb energy of N localized charge distributions. Asymptotically, like the Fast Multipole Method (FMM), the computational cost of the method scales linearly with N. This scaling can be traced to the Laws of Large Numbers and, in particular, to the statistics of the two-dimensional random walk. We have implemented the algorithm on a small workstation and applied it to systems with up to 10(6) charged particles.