Hays was president of the Motion Picture Producers and Distributors of America & namesake of the Hays censorship code. When he arrived in Hollywood in March 1922, the streets were decorated with "bunting and flags and big signs reading 'Welcome, Will Hays!'" 1 Chaplin was the only big-time producer not to attend his reception.
According to his FBI file, in August 1922, Chaplin hosted a party at his studio for future Communist Party chairman, William Z. Foster, which was attended by many "Parlor Bolsheviki" and "radicals," including William DeMille and Chaplin's friend, Rob Wagner. According to the report:
Chaplin stated to Foster that neither himself nor any of the stars associated with him have any use for Will Hays. 'We are against any kind of censorship, and particularly against Presbyterian censorship,' he said laughingly, and showed his guests a pennant with the words "Welcome, Will Hays," which he had fastened over the door of the men's toilet in his studio.2This report was forwarded to Hays who responded by saying that he found Chaplin to be "a little odd in his mental processes, to say the least, in the direction which you mention. I did not know he had gone as far, however, as the report indicates." 3
In 1928, Hays was Chaplin's guest, along with Ambassador Alexander Moore, at the premiere of The Circus (see the video here). I've always thought this was a little strange given Chaplin's opinion of Hays but perhaps this appearance together was nothing more than a pretense. Although Hays evidently attended a dinner at Chaplin's home before the premiere and a party afterwards at the Montmartre.4
1The Memoirs Of Will H. Hays, Doubleday, 1955
2Chaplin's FBI File, part 7, page 4
3Chaplin's FBI File, part 7, page 9
4Boston Globe, Feb. 1, 1928