Based on Article 4 of the 2008 Law on Vietnamese Nationality regulations on nationality principles:

"Article 4. The nationality principle

The State of the Socialist Republic of Vietnam recognizes that Vietnamese citizens have a single nationality, Vietnamese nationality, unless it is otherwise provided for by this Law."

Based on Article 23 of the 2008 Law on Vietnamese Nationality Regulates cases of returning to Vietnamese nationality:

"Article 23. Cases in which restoration of Vietnamese nationality is permitted

1. A person who has lost his/her Vietnamese nationality as prescribed in Article 26 of this Law and applies for restoration of Vietnamese nationality may restore his/her Vietnamese nationality, if he/she falls into any of the following cases:

a/ Having applied for permission to return to Vietnam;

b/ His/her spouse, a natural parent or a natural offspring is a Vietnamese citizen;

c/ Having made meritorious contributions to Vietnam’s national construction and defense;

d/ Being helpful to the State of the Socialist Republic of Vietnam;

e/ Conducting investment activities in Vietnam;

f/ Having renounced Vietnamese nationality for acquisition of a foreign nationality but failing to obtain permission to acquire the foreign nationality.

2. Persons applying for restoration of Vietnamese nationality may not restore Vietnamese nationality, if such restoration is detrimental to Vietnam’s national interests.

3. A person who has been deprived of his/her Vietnamese nationality may only be considered for restoration of Vietnamese nationality for at least 5 years after the date he/she is deprived of Vietnamese nationality.

4. Persons applying for restoration of Vietnamese nationality shall use their previous Vietnamese names, which must be written in the decisions permitting the restoration of Vietnamese nationality.

5. Persons permitted to restore Vietnamese nationality shall renounce their foreign nationality, except for the following persons in special cases, if so permitted by the President, who:

a/ Are spouses, natural parents or natural offsprings of Vietnamese citizens;

b/ Have made meritorious contributions to Vietnam’s national construction and defense;

c/ Are helpful to the State of the Socialist Republic of Vietnam.

6. The Government shall specify conditions on restoration of Vietnamese nationality."

Accordingly, the State of the Socialist Republic of Vietnam only allows Vietnamese citizens to have one nationality, which is Vietnamese nationality, in case a person returns to Vietnam.Vietnamese While holding US citizenship, that person will have to renounce US citizenship.