  We find that the Fe III$\lambda\lambda$2039-2113 spectral feature in quasars
appears systematically redshifted by amounts accountable under the hypothesis
of gravitational redshift induced by the central supermassive black hole. Our
analysis of 27 composite spectra from the BOSS survey indicates that the
redshift and the broadening of the lines in the Fe III$\lambda\lambda$2039-2113
blend roughly follow the expected correlation in the weak limit of
Schwarzschild geometry for virialized kinematics. Assuming that the Fe III UV
redshift provides a measure of $M_{BH}\over R$ (${\Delta \lambda\over
\lambda}\simeq{3\over2}{G\over c^2} {M_{BH}\over R}$) and using different
estimates of the emitting region size, $R$ (either from gravitational
microlensing, reverberation mapping or from the scaling of size with intrinsic
quasar luminosity), we obtain masses for 10 objects which are in agreement
within uncertainties with previous mass estimates based on the virial theorem.
Reverberation mapping estimates of the size of the Fe
III$\lambda\lambda$2039-2113 emitting region in a sample of objects would be
needed to confirm the gravitational origin of the measured redshifts.
Meanwhile, we present a tentative black hole mass scaling relationship based on
the Fe III$\lambda\lambda$2039-2113 redshift useful to measure the black hole
mass of one individual object from a single spectrum.
