We report the first measurement of the elliptic anisotropy ($v_2$) of the charm meson $D^0$ at mid-rapidity ($|y|$,$<$,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 $D^0$ $v_2$ in 0--80% centrality Au+Au collisions can be described by a viscous hydrodynamic calculation for transverse momentum ($p_{rm T}$) less than 4,GeV/$c$. The $D^0$ $v_2$ as a function of transverse kinetic energy ($m_{rm T} - m_0$, where $m_{rm T} = sqrt{p_{rm T}^2 + m_0^2}$) 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 ($2{pi}TD_s$) in the range of $sim$2--12, are able to simultaneously reproduce our $D^0$ $v_2$ result and our previously published results for the $D^0$ nuclear modification factor.
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