I don't have any personal experience with the Chevron Tang since it's a pretty rare fish but I have kept many other tanks in the past and am currently keeping a Sailfin Tang and Kole Tang together. Since they are herbivores, you must include plenty of greens. My tangs have always picked at my live rock because they are completely covered in algae. Since the Kole Tang and Chevron Tang are from the same genus, here is what I noticed. My Kole Tang was picking at the rocks a lot when he was first introduced but he rarely took what I offered. I then put in some dry nori and he loves to pick at that. Since then, he picks at the rocks, nori, and he eats spirulina, formula one, formula two, frozen brine shrimp, and frozen mysis shrimp.
Good luck with your tang.