Born in about 1942, originally from Bellevue, Washington, Parr served as editor of Chess Life magazine, the official publication of the United States Chess Federation, from 1985 to 1988. Later, Parr was the editor of Glasnost magazine, an anti-Soviet periodical. Parr is known as a vehement anti-Communist and classifies himself as a libertarian. Parr is also a fluent speaker of Russian.
Parr is a close friend of Grandmaster Larry Evans and they often collaborate on projects. Parr has played relatively little tournament chess, preferring instead to write books about the subject. In 1991, he collaborated with GM Arnold Denker in writing The Bobby Fischer I Knew And Other Stories.