  We exhibit a topological group $G$ with property (T) acting non-elementarily
and continuously on the circle. This group is an uncountable totally
disconnected closed subgroup of $\operatorname{Homeo}^+(\mathbf{S}^1)$. It has
a large unitary dual since it separates points. It comes from homeomorphisms of
dendrites and a kaleidoscopic construction. Alternatively, it can be seen as
the group of elements preserving some specific geodesic lamination of the
hyperbolic disk.
  We also prove that this action is unique up to conjugation and that it can't
be smoothened in any way. Finally, we determine the universal minimal flow of
the group $G$.
