  While there are well established methods to study delocalization transitions
of single particles in random systems, it remains a challenging problem how to
characterize many body delocalization transitions. Here, we use a generalized
real-space renormalization group technique to study the anisotropic Heisenberg
model with long-range interactions, decaying with a power $\alpha$, which are
generated by placing spins at random positions along the chain. This method
permits a large-scale finite-size scaling analysis. We examine the full
distribution function of the excitation energy gap from the ground state and
observe a crossover with decreasing $\alpha$. At $\alpha_c$ the full
distribution coincides with a critical function. Thereby, we find strong
evidence for the existence of a many body localization transition in disordered
antiferromagnetic spin chains with long range interactions.
