Whitney died of natural causes on Friday in her California home, her son Jonathan Dweck said. She is also survived by another son, Scott.
Whitney starred as Captain Kirk's assistant Yeoman Janice Rand in the first eight episodes of the long-running series. She later reprised her role in the films Star Trek: The Motion Picture, Star Trek III: The Search for Spock, Star Trek IV: The Voyage Home and Star Trek VI: The Undiscovered Country.
According to her 1998 autobiography, she struggled with addiction for years and credits Leonard Nimoy, who starred as Spock in the series, for helping her regain her career. Dweck said she dedicated the last 35 years of her life helping people others with addiction.
William Shatner, who also starred in the series, tweeted his condolences on Monday:
Condolences to the family of Grace. She was a constant shining smile over the years every time our paths crossed.— William Shatner (@WilliamShatner) May 4, 2015