  We investigate when the group $SL_n(\mathcal{O}(X))$ of holomorphic maps from
a Stein space $X$ to $SL_n (\C)$ has Kazhdan's property (T) for $n\ge 3$. This
provides a new class of examples of non-locally compact groups having Kazhdan's
property (T). In particular we prove that the holomorphic loop group of $SL_n
(\C)$ has Kazhdan's property (T) for $n\ge 3$. Our result relies on the method
of Shalom to prove Kazhdan's property (T) and the solution to Gromov's
Vaserstein problem by the authors.
