  The three-dimensional Dirac semimetal is distinct from its two-dimensional
counterpart due to its dimensionality and symmetry. Here, we observe that
molecule-based quasi-two-dimensional Dirac fermion system,
$\alpha$-(BEDT-TTF)$_2$I$_3$, exhibits chiral anomaly-induced negative
magnetoresistance and planar Hall effect upon entering the coherent inter-layer
tunneling regime under high pressure. Time-reversal symmetry is broken due to
the strong electronic correlation effect, while the spin-orbit coupling effect
is negligible. The system provides an ideal platform for investigating the
chiral anomaly physics by controlling dimensionality and strong electronic
correlation.
