  We initiate the study of the spherically symmetric Einstein-Klein-Gordon
system in the presence of a negative cosmological constant, a model appearing
frequently in the context of high-energy physics. Due to the lack of global
hyperbolicity of the solutions, the natural formulation of dynamics is that of
an initial boundary value problem, with boundary conditions imposed at null
infinity. We prove a local well-posedness statement for this system, with the
time of existence of the solutions depending only on an invariant H^2-type norm
measuring the size of the Klein-Gordon field on the initial data. The proof
requires the introduction of a renormalized system of equations and relies
crucially on r-weighted estimates for the wave equation on asymptotically AdS
spacetimes. The results provide the basis for our companion paper establishing
the global asymptotic stability of Schwarzschild-Anti-de-Sitter within this
system.
