  In this paper we consider deformations of an algebroid stack on an etale
groupoid. We construct a differential graded Lie algebra (DGLA) which controls
this deformation theory. In the case when the algebroid is a twisted form of
functions we show that this DGLA is quasiisomorphic to the twist of the DGLA of
Hochschild cochains on the algebra of functions on the groupoid by the
characteristic class of the corresponding gerbe.
