It has been known since 1986 that it is possible to construct simple lattice–gas cellular automata whose hydrodynamics are governed by the Navier–Stokes equations in two dimensions. The simplest such model heretofore known has six bits of state per site on a triangular lattice. In this work, we demonstrate that it is possible to construct a model with only five bits of state per site on a Kagome lattice. Moreover, the model has a simple, deterministic set of collision rules and is easily implemented on a computer. In this work, we derive the equilibrium distribution function for this lattice–gas automaton and carry out the Chapman–Enskog analysis to determine the form of the Navier–Stokes equations.