In this talk, we will present the first measurement of rapidity-odd directed flow (v1) for D0 and anti-D0 mesons at mid-rapidity (|y| < 0.8) in Au+Au collisions at sqrt(sNN) = 200 GeV using the STAR detector at the Relativistic Heavy Ion Collider. In 10-80% Au+Au collisions, the slope of the v1 rapidity dependence (dv1/dy), averaged over D0 and anti-D0 mesons, is -0.080 +/- 0.017 (stat.) +/- 0.016 (syst.) for transverse momentum (pT) above 1.5 GeV/c. The absolute value of D0-meson dv1/dy is about 25 times larger than that for charged kaons, with 3.4sigma significance. These data not only give unique insight into the initial tilt of the produced matter, they are expected to provide improved constraints for the geometric and transport parameters of the hot QCD medium created in relativistic heavy-ion collisions.