  In the half-space model of hyperbolic space, that is,
$\r^3_{+}=\{(x,y,z)\in\r^3;z>0\}$ with the hyperbolic metric, a translation
surface is a surface that writes as $z=f(x)+g(y)$ or $y=f(x)+g(z)$, where $f$
and $g$ are smooth functions. We prove that the only minimal translation
surfaces (zero mean curvature in all points) are totally geodesic planes.
