  The field of topological materials science has recently been focussing on
three-dimensional Dirac semimetals, which exhibit robust Dirac phases in the
bulk. However, the absence of characteristic surface states in accidental Dirac
semimetals (DSM) makes it difficult to experimentally verify claims about the
topological nature using commonly used surface-sensitive techniques. The chiral
magnetic effect (CME), which originates from the Weyl nodes, causes an
$\textbf{E}\cdot\textbf{B}$-dependent chiral charge polarization, which
manifests itself as negative magnetoresistance. We exploit the extended
lifetime of the chirally polarized charge and study the CME through both local
and non-local measurements in Hall bar structures fabricated from single
crystalline flakes of the DSM Bi$_{0.97}$Sb$_{0.03}$. From the non-local
measurement results we find a chiral charge relaxation time which is over one
order of magnitude larger than the Drude transport lifetime, underlining the
topological nature of Bi$_{0.97}$Sb$_{0.03}$.
