  We prove that the group of automorphisms of the generic meet-tree expansion
of an infinite non-unary free Fra\"{\i}ss\'{e} limit over a finite relational
language is simple. As a prototypical case, the group of automorphism of the
Rado meet-tree (i.e. the Fra\"{\i}ss\'{e} limit of finite graphs which are also
meet-trees) is simple.
