  For a Lie groupoid there is an analytic index morphism which takes values in
the $K-$theory of the $C^*$-algebra associated to the groupoid. This is a good
invariant but extracting numerical invariants from it, with the existent tools,
is very difficult. In this work, we define another analytic index morphism
associated to a Lie groupoid; this one takes values in a group that allows us
to do pairings with cyclic cocycles. This last group is related to the
compactly supported functions on the groupoid. We use the tangent groupoid to
define our index as a sort of ''deformation''.
