What geologic action may produce a chain of volcanic islands

The chains of volcanic islands can be found mostly alongside the borders of the convergent plate boundaries, more specifically, on the convergent boundaries between an oceanic and continental tectonic plates. That can easily be seen by the so called ''Ring of Fire'' where there's numerous chains of volcanic islands

a hot spot

Explanation:

Volcanic island chains are formed independently of the movements of tectonic plates. They are found above the hot spots caused by the mantle. Currents of hot materials from the mantle pierce a path through the crust, creating a chain of hot spot volcanoes. They form volcanoes that produce highly fluid lava that build the flat volcanoes of the shield. Example: Mauna loa, Hawaii.