  We propose an experiment to test the Weak Equivalence Principle (WEP) with a
test mass consisting of two entangled atoms of different species. In the
proposed experiment, a coherent measurement of the differential gravity
acceleration between the two atomic species is considered, by entangling two
atom interferometers operating on the two species. The entanglement between the
two atoms is heralded at the initial beam splitter of the interferometers
through the detection of a single photon emitted by either of the atoms,
together with the impossibility of distinguishing which atom emitted the
photon. In contrast to current and proposed tests of the WEP, our proposal
explores the validity of the WEP in a regime where the two particles involved
in the differential gravity acceleration measurement are not classically
independent, but entangled. We propose an experimental implementation using
$^{85}$Rb and $^{87}$Rb atoms entangled by a vacuum stimulated rapid adiabatic
passage protocol implemented in a high finesse optical cavity. We show that an
accuracy below $10^{-7}$ on the E\"otv\"os parameter can be achieved.
