  Thermalized matter created in non-central relativistic heavy-ion collisions
is expected to be tilted in the reaction plane with respect to the beam axis.
The most notable consequence of this forward-backward symmetry breaking is the
observation of rapidity-odd directed flow for charged particles. On the other
hand, the production points for heavy quarks are forward-backward symmetric and
shifted in the transverse plane with respect to the fireball. The drag of heavy
quarks from the asymmetrically distributed thermalized matter generates a large
directed flow for heavy flavor mesons. We predict a very large rapidity odd
directed flow of $D$ mesons in non-central Au-Au collisions at
$\sqrt{s_{NN}}=200$ GeV, $several$ $times$ $larger$ than for charged particles.
A possible experimental observation of a large directed flow for heavy flavor
mesons would represent an almost direct probe of the 3-dimensional distribution
of matter in heavy-ion collisions.
