  Chase-escape is a competitive growth process in which red particles spread to
adjacent empty sites according to a rate-$\lambda$ Poisson process while being
chased and consumed by blue particles according to a rate-$1$ Poisson process.
Given a growing sequence of finite graphs, the critical rate $\lambda_c$ is the
largest value of $\lambda$ for which red fails to reach a positive fraction of
the vertices with high probability. We provide a conjecturally sharp lower
bound and an implicit upper bound on $\lambda_c$ for supercritical random
graphs sampled from the configuration model with independent and identically
distributed degrees with finite second moment. We additionally show that the
expected number of sites occupied by red undergoes a phase transition and
identify the location of this transition.
