A new approach to quantum gravity is described which joins the loop representation formulation of the canonical theory to the causal set formulation of the path integral. The theory assigns quantum amplitudes to special classes of causal sets, which consist of spin networks representing quantum states of the gravitational field joined together by labeled null edges. The theory exists in 3 + 1-, 2 + 1- and 1 + 1- dimensional versions, and may also be interpreted as a theory of labeled timelike surfaces. The dynamics is specified by a choice of functions of the labelings of d + 1- dimensional simplices, which represent elementary future light cones of events in these discrete space-times. The quantum dynamics thus respects the discrete causal structure of the causal sets. In the 1 + 1- dimensional case the theory is closely related to directed percolation models. In this case, at least, the theory may have critical behavior associated with percolation, leading to the existence of a classical limit.