  In this note we characterize compact hypersurfaces of dimension $n\geq 2$
with constant mean curvature $H$ immersed in space forms of constant curvature
and satisfying an optimal integral pinching condition: they are either totally
umbilical or, when $n\geq 3$ and $H\neq 0$, they are locally contained in a
rotational hypersurface. In dimension two, the integral pinching condition
reduces to a topological assumption and we recover the classical Hopf-Chern
result.
