Rhondda Gillespie (4 August 1941 – 30 December 2010) was an Australian-born classical pianist who resided primarily in the United Kingdom and Barbados. She was a specialist in the music of Franz Liszt and brought to light many of his lesser-known works. She was also renowned for her focus on contemporary music, and she gave many world premieres of British music.
Rhondda Marie Gillespie was born in Sydney in 1941. She was an only child. At the age of 8 she played Manuel de Falla's Ritual Fire Dance on Jack Davey's radio show Star Search. She gave her first public recital at 12. Her formal studies were at the Sydney Conservatorium of Music under Alexander Sverjensky (where her fellow students included Malcolm Williamson, Richard Farrell and Roger Woodward) and in Britain under Louis Kentner and Denis Matthews.
She won the Harriet Cohen Commonwealth Medal in 1959. 
Wilfred Josephs' 14 Studies for Piano, Op. 53 were written for Rhondda Gillespie, Joy Blech and Yonty Solomon. Gillespie gave the world premiere of the complete set at the Cheltenham Festival in 1967.
In 1976, for Joseph Horovitz's 50th birthday, Rhondda Gillespie played his Jazz Concerto at the Queen Elizabeth Hall.  She played Franz Liszt's piano transcription of Hector Berlioz's Symphonie fantastique at the 1977 London Liszt Festival. With the actor Michael Gough she also gave the first complete performance in London of Liszt's dramatic recitations.
In 1984 Rhondda Gillespie and her fellow Australian pianist Robert Weatherburn formed a professional duo to present repertoire for piano four-hands and two pianos. They toured Malta and England and appeared in Sydney. There they premiered John Dankworth's Fantasia Enigmatica in 1986. In 1987, at the Sydney Opera House, they gave the world premieres of Weatherburn's arrangement for two pianos of Liszt's Geharnischte Lied and of his own composition for two pianos, Mnajdra.  They gave the Southern Hemisphere premiere of Liszt's Concerto pathétique for 2 pianos. For Malcolm Arnold's 70th birthday they played his Concerto for Piano Four-hands and Strings, and for his 80th birthday the Concerto for Two Pianos and Orchestra. Miriam Hyde and other composers wrote works for Gillespie and Weatherburn. 
Rhondda Gillespie ceased playing in the 1990s due to arthritis in her fingers. She had come to spend much of her time (including the English winters) in Barbados, where she died on 30 December 2010, aged 69.  Her former husband Denby Richards had died on 7 December.
Rhondda Gillespie's recordings included:
- the world premiere recordings of the piano sonatas by Constant Lambert (1974) and Sir Arthur Bliss
- Usko Meriläinen's First Piano Concerto (Royal Philharmonic Orchestra under Walter Susskind)
- Franz Liszt's Weihnachtsbaum, Sonata in B minor, Consolations and 2 Ballades
- music by Charles Camilleri, Percy Grainger and Johann Sebastian Bach.
- Chandos; Retrieved 1 June 2013
- Australian Women's Weekly, 16 December 1970; Retrieved 1 June 2013
- "Concert pianist brought lesser-known Liszt pieces to life", Sydney Morning Herald, 2 February 2011; Retrieved 1 June 2013
- Music Web International; Retrieved 1 June 2013
- International Who's Who in Music and Musicians Directory 2000/2001; Retrieved 1 June 2013
- Tribute to Denby Richards, Musical Opinion; Retrieved 1 June 2013
- Robert Weatherburn website; Retrieved 1 June 2013
- classical source; Retrieved 1 June 2013
- Lisa Hardy, The British Piano Sonata 1870-1945; Retrieved 1 June 2013