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Doctors in the southern province of Tien Giang say the girl, born weighing just over eight pounds, was born on Monday.
She is 27-year-old Nguyen Bich Thuy and her husband's first child.
The baby has been moved to a hospital in Vietnam's capital, Ho Chi Minh City, where she will be closely observed.
Doctors are not speculating on what her chances of survival are.
A Vietnamese newspaper, Tuoi Tre, carried a picture of the baby on Thursday.
Very rare
It is very rare for babies to be born with two heads - let alone two hearts and spines.
Experts calculate that only one in two million children are born with two heads.
The deformity is usually caused by a single fertilised egg failing to divide to form two separate twins.
The operation to separate heads is one of the most difficult to perform, given the huge complexity of the brain.
An American scientist is thought to have performed the first operation to part twins joined at the head without causing them significant brain damage. The operation took place in South Africa in December.
Most Siamese twins are born joined at the chest. The most famous recent case was of American twins Amy and Angela Lakeberg.
Born in 1993, they were joined at the chest, liver and heart. Both died.
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