  We use functional renormalization group methods to study gravity minimally
coupled to a free scalar field. This setup provides the prototype of a
gravitational theory which is perturbatively non-renormalizable at one-loop
level, but may possess a non-trivial renormalization group fixed point
controlling its UV behavior. We show that such a fixed point indeed exists
within the truncations considered, lending strong support to the conjectured
asymptotic safety of the theory. In particular, we demonstrate that the
counterterms responsible for its perturbative non-renormalizability have no
qualitative effect on this feature.
