  We introduce the notions of Atiyah class and Todd class of a differential
graded vector bundle with respect to a differential graded Lie algebroid. We
prove that the space of vector fields on a dg-manifold with homological vector
field $Q$ admits a structure of L-infinity algebra with the Lie derivative
$L_Q$ as unary bracket, and the Atiyah cocycle corresponding to a torsion-free
affine connection as binary bracket.
