If such situation happens to you, how would you react? What a person even can do in this situation? Go away with chips? Give chips to someone else and let him cash out? Contact lawyer?
Being calm would be better than being furious when this happens. What you can only do during this situation is to file a formal complaint on that casino. If you know you've won fairly, you won't be afraid doing such thing.
Wait for the casino management to respond and see their reason why they wouldn't allow to exchange your casino chips. If you think something is not right then better course would be to contact your lawyer.
First and foremost, it’s hard to remain calm when you think you are being cheated while you make sure to yourself that you are betting fair and square. So I would say getting angry to the casino would be normal, but it’s always better to not put everything within your hands but chose the legal way. Sue them if you have seen some illegalities on their operation, and since it’s a big threat for them, maybe they will decide to pay you without hassles.
Sometimes, a bad casino will try to take advantage on you, but if you are wise and smart, you will never fall on their trap, so more than a responsible gambler, you also have to be wise and cautious so you will never be outsmarted.