I see what you mean. It is interesting that, according to the reference from above, 'chao' in Japanese is linked to 'ciao' but not the one from Vietnamese. I would not be surprised if the Vietnamese did not get it from the French who got it from the Italians! Enjoy the lingot!
Did I miss anything? Do you know of any Vietnamese links/ties to Portugal/Brazil prior to modern times? If I had to pick a second source, it would have been Japan. Of course, my assumption that a common expression as "Hello" would go further than modern times (given the divergence in political views during modern era as well as the lack of "official" origin of the word) could very well be wrong.
If anything (this is merely a hypothesis), the link would be somewhere from French, which I have yet to study. Since Vietnam was colonized under the French, it is very likely that if French, a Romance language like Italian and Portuguese (which both have Ciao and Tchau respectively), had such an expression, it's also likely that Vietnam would have picked it up. Now that I think about it, if my hypothesis is true, then maybe the other French Indochinese countries may have it too. This is a good question to research.
It was simply because of colonialism, trade and migration (pre-1945 period). Words don't usually sound similar and mean the same concept by chance. The constant moving and trading among people of Asia in those early days played an important role. For example, I learned that Thai, Vietnamese and Indonesian languages all carry some words originated from Cantonese due to the migration of people from southeastern part of China in 19th century.
That makes sense. Similar stories occurred in Europe, Africa, South America and few other places. The fun puzzle to me is to figure out some of the basic words that preserved their meaning across cultures. For example, I am amazed on how thousands of years old Hebrew concepts are preserved in the Chinese language...