In 1955 President Eisenhower sent economic aid and ~700 military personnel to the government of South Vietnam. This effort was foundering in 1960 when John F. Kennedy was elected president.
In May 1961 Kennedy authorized sending an additional 500 Special Forces troops and military advisors to assist the pro Western government of South Vietnam.
By the end of 1962, there were approximately 11,000 military advisors in South Vietnam—that year, 53 military personnel were killed. By the end of 1963, the numbers of military advisors to the South Vietnamese Army had risen to 16,000.
Source: JFK Library