Yes, almost certainly. Much better chance if the chevron is established first. Maybe get the purple tang out til the chevron gets established. Still might not work. The bigger the tank and the more distractions, the better
Honestly your PURPLE TANG will DESTROY the Chevron Tang.
Purple tangs are beautiful fish but extremely aggressive.
I have a 265 gallon and I believe that's not a big enough tank for the aggressive nature of a Purple Tang when it finds a fish it starts to pick on.
The Purple Tang is a very bond fish and will attack the Chevron Tang I believe and if it does picks on your Chevron Tang eventually the Chevron will get stress and stop eating and it's all downhill from there and that will be such a waste of a beautiful fish.
Don't get me wrong others in the hobby are able to get certain fish together that others or I can't get together in 1 system but I don't think it's worth the risk especially with such a beautiful fish like the Chevron Tang.
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Will add that I like to push the boundaries, the norms, the "rules". Have paired many fish that are supposed to be a no go. In this case I would be more than surprised if it works, and would like for you to keep us updated if it does.
Da2145R. it will work 90% if you follow what someone already said get a plastic container from Walmart I drilled holes and place the chevron inside the container and leave it in the tank for a least 3 to 4 days. place it in the middle so that purple and all the fish has to swim thru and get used to it. done it over 10,000 times I deal with fish on a daily basis. then again 90% of the time will work. also when you release it will be maybe some aggression, which is normal wha I do is stay there as don king, and when the purple goes at it deflect it with a bit of food so that purple tang now sees that his food share is not compromise by the new fish. remember fish sees is my habitat and my food thats what is in their mind. now you have to tackle that.