In evolutionary biology, adaptive radiation is a process in which organisms diversify rapidly from an ancestral species into a multitude of new forms, particularly when a change in the environment makes new resources available, creates new challenges, or opens new environmental niches.
The key-innovation that can lead a species to go through rapid adaptive evolution might well be an initial beneficial mutation. You might want to rad about these key-innovations at Salzburger et al. (2005).
As an example, much of the diversification in ciclid fishes is thought to be driven by jaw morphology driven by a few key genes (a ligand; bmp4, a receptor; bmpr1b and an antagonist; nog2; Brawand et al., 2014). While I don't know the literature well on the topic, it sounds plausible to me that a key mutation may have allowed for the diversity of jaw morphology to diversify (which lead lineages to diversify).
Note, I am aware, I focused my answer on diversification and not on single lineage adaptation per se but I do not know better examples (or a better concept) of a single mutation that could lead to a "chain of beneficial mutations".