Farrah Fawcett was nominated for a Golden Globe* for her work in Poor Little Rich Girl: The Barbara Hutton Story (a 1987 NBC mini-series). The series did win the Golden Globe for Best Mini-Series or Motion Picture Made for TV - Poor Little Rich Girl tied with Escape from Sobibor (1987) (TV).

 

Barbara Hutton inherited $40 million dollars at the ripe age of 6. At 18, she went to Europe and at 29 she married Cary Grant. Miss Hutton married eight times and at sixty-five she died with only $3,500.00 in the bank. The cast includes: David Ackroyd as Graham Mattison, Burl Ives as F.W. Woolworth, Bruce Davison as Jimmy Donahue (Barbara's best friend), and Anne Francis as Marjorie Post Hutton. 

* Best Performance by an Actress in a Mini-Series or Motion Picture Made for TV

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From Wikipedia: Poor Little Rich Girl: The Barbara Hutton Story is a 1987 television biographical drama starring Farrah Fawcett. The film chronicles the life of Barbara Hutton, who was one of the richest American socialite women, but was never happy. Released in two versions, as a TV miniseries and TV movie, the project was based on a book by C. David Heymann.

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Fawcett's performance earned her her fifth Golden Globe Award nomination, for Best Performance by an Actress in a Mini-Series or Motion Picture Made for TV. The film won a Golden Globe Award for Best Miniseries or Television Film and three Emmy Awards, for Hairstyling, Makeup and Costume Design in a Miniseries or a Special