  We start studying chiral algebras (as defined by A. Beilinson and V.
Drinfeld) from the point of view of deformation theory. First, we define the
notion of deformation of a chiral algebra on a smooth curve $X$ over a bundle
of local artinian commutative algebras on $X$ equipped with a flat connection
(whereas `usual' algebraic structures are deformed over a local artinian
algebra) and we show that such deformations are controlled by a certain *-Lie
algebra $\mathfrak g$. Then we try to contemplate a possible additional
structure on $\mathfrak g$ and we conjecture that this structure up to homotopy
is a chiral analogue of Gerstenhaber algebra, i.e. a coisson algebra with odd
coisson bracket (in the terminology of Beilinson-Drinfeld). Finally, we discuss
possible applications of this structure to the problem of quantization of
coisson algebras.
