Tracking an underwater chain using an autonomous vehicle can be a first step towards more efficient solutions for cleaning and inspecting mooring chains. We propose to use a forward looking sonar as a primary perception sensor to enable the vehicle operation in limited visibility conditions and overcome the turbidity arisen during marine growth removal. Despite its advantages, working with acoustic imagery raises additional challenges to the involved image processing and control methodologies. In this paper we present a robust framework to perform chain following, combining perception, planning and control disciplines. We first introduce a detection system that exploits the sonar's high frame rate and applies local pattern matching to handle the complexity of detecting link chains in acoustic images. Then, a planning system deals with the dispersed detections and determines the link waypoints that the vehicle should reach. Finally, the vehicle is guided through these waypoints using a high level controller that has been tailored to simultaneously traverse the chain and keep track of upcoming links. Experiments on real data demonstrate the capability of autonomously follow a chain with sufficient accuracy to perform subsequent cleaning or inspection tasks.