Here is Joseph Stiglitz reflecting  (HT: John Papola) on Martin Luther King and discrimination, indicts Gary Becker:
Another Nobel laureate of the Chicago School, Gary S. Becker , would attempt to show how in truly competitive labor markets discrimination couldn’t exist. While I and others wrote multiple papers explaining the sophistry in the argument, his was an argument that fell on receptive ears.
Here is a better summary of Becker’s views from his bio at the Concise Encyclopedia of Economics :
Becker’s unusually wide applications of economics started early. In 1955 he wrote his doctoral dissertation at the University of Chicago on the economics of discrimination . Among other things, Becker successfully challenged the Marxist view that discrimination helps the person who discriminates. Becker pointed out that if an employer refuses to hire a productive worker simply because of skin color, that employer loses out on a valuable opportunity. In short, discrimination is costly to the person who discriminates.
Becker showed that discrimination will be less pervasive in more competitive industries because companies that discriminate will lose market share to companies that do not. He also presented evidence that discrimination is more pervasive in more-regulated, and therefore less-competitive, industries. The idea that discrimination is costly to the discriminator is common sense among economists today, and that is due to Becker.