Regeneration after peripheral nerve damage requires that axons re-grow to the correct target tissues in a process called target-specific regeneration. Although much is known about the mechanisms that promote axon re-growth, re-growing axons often fail to reach the correct targets, resulting in impaired nerve function. We know very little about how axons achieve target-specific regeneration, particularly in branched nerves that require distinct targeting decisions at branch points. The zebrafish vagus motor nerve is a branched nerve with a well-defined topographic organization. Here, we track regeneration of individual vagus axons after whole-nerve laser severing and find a robust capacity for target-specific, functional re-growth. We then develop a new single-cell chimera injury model for precise manipulation of axon-environment interactions and find that (1) the guidance mechanism used during regeneration is distinct from the nerve's developmental guidance mechanism, (2) target selection is specified by neurons' intrinsic memory of their position within the brain, and (3) targeting to a branch requires its pre-existing innervation. This work establishes the zebrafish vagus nerve as a tractable regeneration model and reveals the mechanistic basis of target-specific regeneration.