  We rigorously construct the first steady traveling wave solutions of the 2D
incompressible Euler equation that take the form of a contiguous vortex-patch
dipole, which can be viewed as the vortex-patch counterpart of the well-known
Lamb-Chaplygin dipole. Our construction is based on a novel fixed-point
approach that determines the patch boundary as the fixed point of a certain
nonlinear map. Smoothness and other properties of the patch boundary are also
obtained.
