Magneto-optic Kerr-effect measurements (bulk sensitive) and spin-polarized low-energy electron diffraction (surface sensitive) reveal that the surface and the bulk Curie temperatures of epitaxial EuS(111) on Si(111) are identical to within \ifmmode\pm\else\textpm\fi{}0.04 K. In the critical region of the bulk, the surface magnetization ${m}_{1}$ of this model substance for an isotropic Heisenberg ferromagnet decreases as ${m}_{1}\ensuremath{\sim}{(1\ensuremath{-}\frac{T}{{T}_{C}})}^{{\ensuremath{\beta}}_{1}}$, with ${\ensuremath{\beta}}_{1}=0.72\ifmmode\pm\else\textpm\fi{}0.03$. This differs significantly from current theoretical estimates of ${\ensuremath{\beta}}_{1}$, possibly pointing to a very strong surface anisotropy.