© 2017 American Physical Society. We report the first measurement of the elliptic anisotropy (v2) of the charm meson D0 at midrapidity (|y|<1) in Au+Au collisions at sNN=200 GeV. The measurement was conducted by the STAR experiment at RHIC utilizing a new high-resolution silicon tracker. The measured D0 v2 in 0%-80% centrality Au+Au collisions can be described by a viscous hydrodynamic calculation for a transverse momentum (pT) of less than 4 GeV/c. The D0 v2 as a function of transverse kinetic energy (mT-m0, where mT=pT2+m02) is consistent with that of light mesons in 10%-40% centrality Au+Au collisions. These results suggest that charm quarks have achieved local thermal equilibrium with the medium created in such collisions. Several theoretical models, with the temperature-dependent, dimensionless charm spatial diffusion coefficient (2πTDs) in the range of ∼2-12, are able to simultaneously reproduce our D0 v2 result and our previously published results for the D0 nuclear modification factor.