  We show that any compact quaternionic contact (qc) hypersurfaces in a
hyper-K\"ahler manifold which is not totally umbilical has an induced qc
structure, locally qc homothetic to the standard 3-Sasakian sphere. We also
show that any nowhere umbilical qc hypersurface in a hyper-K\"ahler manifold is
endowed with an involutive 7-dimensional distribution whose integral leafs are
locally qc-conformal to the standard 3-Sasakian sphere.
