We introduce a new combinatorial construction, called a dual equivalence graph, based on Haiman's 1992 discovery of an equivalence relation on tableaux which is "dual" to jeu-de-taquin. We define a generating function on the vertices of such graphs and show that it is always Schur positive. We outline the construction of a graph on standard $k$-tuples of young tableaux which we prove is a dual equivalence graph for $k \leq 3$. This gives a combinatorial description of the Schur coefficients of the ribbon tableaux generating functions introduced by Lascoux, Leclerc and Thibon. Recalling Haglund's monomial expansion for Macdonald polynomials, we conclude with a combinatorial formula for the Schur expansion of Macdonald polynomials indexed by a partition with at most 3 columns.