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A decisive experimental test of the Chiral Magnetic Effect (CME) is
considered one of the major scientific goals at the Relativistic Heavy-Ion
Collider (RHIC) towards understanding the nontrivial topological fluctuations
of the Quantum Chromodynamics vacuum. In heavy-ion collisions, the CME is
expected to result in a charge separation phenomenon across the reaction plane,
whose strength could be strongly energy dependent. The previous CME searches
have been focused on top RHIC energy collisions. In this Letter, we present a
low energy search for the CME in Au+Au collisions at $\sqrt{s_{_{\rm{NN}}}}=27$
GeV. We measure elliptic flow scaled charge-dependent correlators relative to
the event planes that are defined at both mid-rapidity $|\eta|<1.0$ and at
forward rapidity $2.1 < |\eta|<5.1$. We compare the results based on the
directed flow plane ($\Psi_1$) at forward rapidity and the elliptic flow plane
($\Psi_2$) at both central and forward rapidity. The CME scenario is expected
to result in a larger correlation relative to $\Psi_1$ than to $\Psi_2$, while
a flow driven background scenario would lead to a consistent result for both
event planes. In 10-50\% centrality, results using three different event planes
are found to be consistent within experimental uncertainties, suggesting a flow
driven background scenario dominating the measurement. We obtain an upper limit
on the deviation from a flow driven background scenario at the 95\% confidence
level. This work opens up a possible road map towards future CME search with
the high statistics data from the RHIC Beam Energy Scan Phase-II.