  We study constant mean curvature graphs in the Riemannian 3-dimensional
Heisenberg spaces ${\cal H}={\cal H}(\tau)$. Each such ${\cal H}$ is the total
space of a Riemannian submersion onto the Euclidean plane $\mathbb{R}^2$ with
geodesic fibers the orbits of a Killing field. We prove the existence and
uniqueness of CMC graphs in ${\cal H}$ with respect to the Riemannian
submersion over certain domains $\Omega\subset\mathbb{R}^2$ taking on
prescribed boundary values.
