  We show that constant mean curvature hypersurfaces in $\mathbb
H^n\times\mathbb R$, with small and pinched boundary contained in a horizontal
slice $P$ are topological disks, provided they are contained in one of the two
halfspaces determined by $P$. This is the analogous in $\mathbb
H^n\times\mathbb R$ of a result in $\mathbb R^3$ by A. Ros and H. Rosenberg.
