Ray Garrett Jr., 59, a Chicago attorney who was chairman of the Securities and Exchange Commission from 1973 to 1975, died of cancer Sunday in a hospital in Evanston, Ill.

During his years as chairman, he played a major role in the abolition of fixed brokerage commissions rates. He also began moving the nation's securities toward a more efficient electronic nationwide system.

Mr. Garrett was a partner in the Chicago law firm of Gardner, Carton & Douglas. At the time of his death, he was vice chairman of the public oversight board of the American Institute of Public Accountants and a member of the legal advisory committee of the board of directors of the New York Stock Exchange.

He had chaired several committees of the American Bar Association, been a fellow of the American Bar Foundation and belonged to the Illinois and Chicago bar associations.

Mr. Garrett was a native of Chicago. He was a graduate of Yale University and earned a law degree at Harvard University. He served as a captain in the Army's field artillery during World War II and earned the Bronze Star medal.

Following the war, he taught law at New York University and practiced law in Chicago before coming to Washington in 1952 and joining the staff of the SEC. Two years later he was named director of the Commission's Division of Corporate Regulation, a post he held until returning to private practice in Chicago in 1958.

Mr. Garrett was a resident of Winnetka, Ill., and a member of the Metropolitan Club in Washington.

Survivors include his wife of 37 years, Virginia; of Winnertka; three daughters, Nancy Worcester of San Diego; Susan Dunn of San Antonio, and Anne Burfield of Reston; a son, Richard, of Minneapolis; two sisters, Glenn Lindgren of Boston, and Martha Benson of Denver, and six grandchildren.