  We present an analytical calculation of the leading three-loop radiative
correction to the rho-parameter in the Standard Model in the large Higgs mass
limit. This correction, of order g^6 m_H^4/M_W^4, is opposite in sign to the
leading two-loop correction of order g^4 m_H^2/M_W^2. The two corrections
cancel each other for a Higgs mass of approximately 480 GeV. The result shows
that it is extremely unlikely that a strongly interacting Higgs sector could
fit the data of electroweak precision measurements.
