The 1880 federal census did identify, however, three restaurants operated by Chinese. But should they be considered "Chinese restaurants" since it is highly unlikely that they would have served or their customers would have wanted Chinese food. Remember, even chop suey, the dish that became the most popular or at least well known offering for non-Chinese was totally unknown anywhere in the U. S. until around 1900.
In the clippings below, we see that Nee Gaw was a restaurant keeper (the census taker's term) in Yazoo City, and he had 2 cooks born in China to Chinese parents. In Leflore, 2 brothers ran a restaurant (their names got mangled by the census taker and don't look Chinese, but the record indicates they were born in China to Chinese parents) And, in Silver City, 20 year old Henry Hong was a restaurant keeper.
So, in one sense these are "Chinese" restaurants, but in another sense, they are not. They are just restaurants operated by Chinese that served American food and probably nothing resembling Chinese food. But since we have no access to their menus, who knows for sure?