A Weyl group multiple Dirichlet series is a Dirichlet series in several complex variables attached to a root system . The number of variables equals the rank r of the root system, and the series satisfies a group of functional equations isomorphic to the Weyl group W of . In this paper we construct a Weyl group multiple Dirichlet series over the rational function field using nth order Gauss sums attached to the root system of type A2. The basic technique is that of [8, 9]; namely, we construct a rational function in r variables invariant under a certain action of W, and use this to build a “local factor” of the global series.