In this work we extend the theory of the classical Hardy space H 1 to the rational Dunkl setting. Specifically, let ∆ be the Dunkl Laplacian on a Euclidean space R N. On the half-space R + ×R N , we consider systems of conjugate (∂ 2 t +∆ x)-harmonic functions satisfying an appropriate uniform L 1 condition. We prove that the boundary values of such harmonic functions, which constitute the real Hardy space H 1 ∆ , can be characterized in several different ways, namely by means of atoms, Riesz transforms, maximal functions or Littlewood-Paley square functions.