Summary: This article presents a rigorous existence theory for three-dimensional gravity-capillary water waves which are uniformly translating and periodic in one spatial direction \(x\) and have the profile of a uni- or multipulse solitary wave in the other \(z\). The waves are detected using a combination of Hamiltonian spatial dynamics and homoclinic Lyapunov-Schmidt theory. The hydrodynamic problem is formulated as an infinite-dimensional Hamiltonian system in which \(z\) is the timelike variable, and a family of points \(P_{k,k+1}\), \(k = 1,2,\dots\) in its two-dimensional parameter space is identified at which a Hamiltonian \(0^20^2\) resonance takes place (the zero eigenspace and generalised eigenspace are respectively two and four dimensional). The point \(P_{k,k+1}\) is precisely that at which a pair of two-dimensional periodic linear travelling waves with frequency ratio \(k:k+1\) simultaneously exist (“Wilton ripples”). A reduction principle is applied to demonstrate that the problem is locally equivalent to a four-dimensional Hamiltonian system near \(P_{k,k+1}\). It is shown that a Hamiltonian real semisimple \(1:1\) resonance, where two geometrically double real eigenvalues exist, arises along a critical curve \(R_{k,k+1}\) emanating from \(P_{k,k+1}\). Unipulse transverse homoclinic solutions to the reduced Hamiltonian system at points of \(R_{k,k+1}\) near \(P_{k,k+1}\) are found by a scaling and perturbation argument, and the homoclinic Lyapunov-Schmidt method is applied to construct an infinite family of multipulse homoclinic solutions which resemble multiple copies of the unipulse solutions.