The field of topological materials science has recently been focusing on three-dimensional Dirac semimetals, which exhibit robust Dirac phases in the bulk. However, the absence of characteristic surface states in accidental Dirac semimetals (DSMs) 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 E·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 nonlocal measurements in Hall bar structures fabricated from single crystalline flakes of the DSM Bi0.97Sb0.03. From the nonlocal 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 Bi0.97Sb0.03.