  Topological Dirac semimetal is a newly discovered class of materials and has
attracted intense attentions. This material can be viewed as a
three-dimensional (3D) analogue of graphene and has linear energy dispersion in
bulk, leading to a range of exotic transport properties. Here we report direct
quantum transport evidence of 3D Dirac semimetal phase of layered material
ZrTe5 by angular dependent magnetoresistance measurements under high magnetic
fields up to 31 Tesla. We observed very clear negative longitudinal
magnetoresistance induced by chiral anomaly under the condition of the magnetic
field aligned only along the current direction. Pronounced Shubnikov-de Hass
(SdH) quantum oscillations in both longitudinal magnetoresistance and
transverse Hall resistance were observed, revealing anisotropic light cyclotron
masses and high mobility of the system. In particular, a nontrivial {\pi}-Berry
phase in the SdH gives clear evidence for 3D Dirac semimetal phase.
Furthermore, we observed clear Landau Level splitting under high magnetic
field, suggesting possible splitting of Dirac point into Weyl points due to
broken time reversal symmetry. Our results indicate that ZrTe5 is an ideal
platform to study 3D massless Dirac and Weyl fermions in a layered compound.
