Reilly was born in The Bronx, New York City, New York, United States, North America, the son of Charles Joseph Reilly, an Irish Catholic commercial artist, and Signe Elvera Nelson, a Swedish Lutheran. When young, he would often make his own puppet theater to amuse himself. His mother, foreshadowing his future as an entertainer, often would tell him to "save it for the stage". At age 13, he survived the 1944 Hartford Circus Fire, which killed 169 people in Connecticut.

Magazine and newspaper profiles of Reilly throughout the 1970s and 1980s did not mention his personal life or sexuality. Many years after the cancellation of Match Game, he revealed his homosexuality in his theatrical one-man show, Save It for the Stage: The Life of Reilly.  Much like fellow game-show regular Paul Lynde of the same era, despite Reilly's off-camera silence, he gave signals on-camera of a campy persona. In many episodes of Match Game, he lampooned himself by briefly affecting "YO!" in a deep voice and the nickname "Chuck" and self-consciously describing how "butch" he was. Many years after his game show career ended, he mentioned in a 2002 interview with Entertainment Tonight that he felt no need to explain his joke about "Chuck", and that he never purposely hid being gay from anyone. Patrick Hughes III, a set decorator and dresser, was Reilly's domestic partner; the two met backstage while Reilly appeared on the game show Battlestars, although their partnership was not revealed publicly. They lived together in Beverly Hills.  Despite sporting what appeared to be a full head of hair for most of the prime of his television career, Reilly was in fact bald, wearing a toupee throughout most of his appearances in the 1970s and 1980s. During the taping of Match Game 74, his toupee became the joke of the filming when Reilly had to go to New York City to have his toupee adjusted. During the taping of several episodes, Reilly was seen wearing different hats because his toupee was back in New York waiting for him to be fitted. This was the start of the long-running jokes on Match Game about his hair. He abandoned the toupee in the late 1990s and appeared bald in public for the rest of his life. He dramatized the experience in his stage show The Life of Reilly. In one episode of Match Game '78, he took off his toupee and gave it to a bald contestant by putting it on his head. One can briefly see Reilly's bald head as he rushed back to his seat and put on a hat to cover up.  In one of his several appearances on The Tonight Show, Reilly publicly discussed having to fix or adjust his toupee before going out for the evening. Among his revelations to Carson while a guest on the show were: that he had nothing to wear but a specific tuxedo; his stories as a director of a play; and how wonderful many of the other guests on that night's panel were when Reilly had worked with them, either in film or in the theater.

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