Born in New York in 1936, Randall grew up in New Mexico before living for twenty-three years in Mexico, Cuba, and Nicaragua. In Mexico she co-founded and edited El corno emplumado/The Plumed Horn, a vanguard bilingual literary journal of the 1960s. In Cuba and Nicaragua she worked with other artists to contribute to social change. Randall returned to the U.S. in 1984, only to face attacks on her writing that led to an effort to deport her under the McCarran-Walter Immigration and Nationality Act. After a five-year battle, joined by many of the nation's outstanding artists, writers, unionists, religious leaders, and others, she won her case in 1989.