This situation arose recently where my Kineticist was firing a Chain Lightning blast at an enemy who was under the effects of a Mirror Image spell. The lightning struck an image, and we were not sure whether it could even continue on to another target or if it would simply destroy the image and then end.
The entry in the Mirror Image sidebar regarding Cleave (you "can’t cleave to an image as if it were an actual creature") and in the spell text itself regarding spell touch attacks ("Spells that require a touch attack are harmlessly discharged if used to destroy a figment") lead me to think that the Chain Lightning would in fact end after striking an image, but I wondered if there was an official ruling.