John Martin Tchicai (born April 28, 1936) is a Danish jazz saxophonist. He was one of the earliest European free jazz musicians. He is of Danish and Congolese descent.

Tchicai studied violin in his youth, and in his mid-teens began playing clarinet and alto saxophone, focusing on the latter. By the late 1950's he was travelling around northern Europe, playing with many musicians.

After moving to New York City in 1963, Tchicai fell into the free jazz scene, co-forming the New York Contemporary Five and the New York Art Quartet, and playing on John Coltrane's epochal Ascension.

He returned to Denmark in 1966, and shortly thereafter focused most of his time on music education.

Tchicai returned to a regular gigging and recording schedule in the late 1970's. In the early 1980's he switched to the tenor saxophone as his primary instrument. In 1990 he was awarded a lifetime grant from the Danish Ministry of Culture. Tchicai and his wife relocated to the San Francisco area in 1991, where he has led several ensembles. He was awarded a National Endowment for the Arts fellowship in 1997. He is a member of Henry Kaiser and Wadada Leo Smith's "Yo Miles" band, a loose aggregation of musicians exploring Miles Davis's post-Bitches Brew electric music.