  We propose and apply a new test of Einstein's Equivalence Principle (EEP)
based on the gravitational redshift induced by the central super massive black
hole of quasars in the surrounding accretion disk. Specifically, we compare the
observed gravitational redshift of the Fe III$\lambda\lambda$2039-2113 emission
line blend in quasars with the predicted values in a wide, uncharted, cosmic
territory ($0 \lesssim z_{cosm}\lesssim3$). For the first time we measure, with
statistical uncertainties comparable or better than those of other classical
methods outside the Solar System, the ratio between the observed gravitational
redshifts and the theoretical predictions in 10 independent cosmological
redshift bins in the $1 \lesssim z_{cosm}\lesssim3$ range. The average of the
measured over predicted gravitational redshifts ratio in this cosmological
redshift interval is $\langle z^m_g/z_g^p\rangle=1.05\pm 0.06$ with scatter
$0.13\pm 0.05$ showing no cosmological evolution of EEP within these limits.
This method can benefit from larger samples of measurements with better S/N
ratios, paving the way for high precision tests (below 1\%) of EEP on
cosmological scales.
