Measurement of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>D</mml:mi><mml:mn>0</mml:mn></mml:msup></mml:math> Azimuthal Anisotropy at Midrapidity in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>Au</mml:mi><mml:mo>+</mml:mo><mml:mi>Au</mml:mi></mml:mrow></mml:math> Collisions at <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msqrt><mml:mrow><mml:msub><mml:mrow><mml:mi>s</mml:mi></mml:mrow><mml:mrow><mml:mi>N</mml:mi><mml:mi>N</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:msqrt><mml:mo>=</mml:mo><mml:mn>200</mml:mn><mml:mtext> </mml:mtext><mml:mtext> </mml:mtext><mml:mi>GeV</mml:mi></mml:mrow></mml:math>

We report the first measurement of the elliptic anisotropy (v_{2}) of the charm meson D^{0} at midrapidity (|y|<1) in Au+Au collisions at sqrt[s_{NN}]=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 a transverse momentum (p_{T}) of less than 4 GeV/c. The D^{0} v_{2} as a function of transverse kinetic energy (m_{T}-m_{0}, where m_{T}=sqrt[p_{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 (2πTD_{s}) in the range of ∼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.