  We construct an expanding gradient Ricci soliton in dimension three over the
topological manifold R x T^2 (the product of a line and a torus) that aproaches
asymptotically a constant curvature cusp at one end, and a flat manifold on the
other end. We prove that this is the only gradient soliton with this topology,
provided the curvature is negatively pinched, -1/4 < sec < 0, at the time-zero
manifold (normalizing the soliton to be born at time -1).
