Washington art dealer Chris Middendorf is no longer a financial backer of just any old boxer; he now owns a piece of the new International Boxing Federation light heavyweight champion of the world. His fighter, Prince Charles Williams, won the title with a 10th-round TKO this week from Bobby Czyz.

Middendorf, who was attending his first fight, thought for a few rounds that he might have made a bad deal when he traded an abstract painting for a share of Williams. He described how Williams was knocked to the canvas in the first round and was standing on rubbery legs at the bell. In the second, Czyz nearly knocked him from the ring. "I was very depressed," Middendorf said. "I had met him just before the fight."

Middendorf said he and his wife Alexandra were at ringside and, seeing and hearing the blows land, "I developed a new respect for the power of the punch." Now he is so enthusiastic about his boxer that he wants Williams to take on the first challenge to his title in Washington. As for his investment, Middendorf says the fighter "has to be the best trade I ever made for a painting." Out & About

Playboy magazine is coming to town this week to interview for an uncoming undraped photo essay titled "The Women of Washington" to be published sometime in 1988. Those interviews, however, won't be at Georgetown's Four Seasons Hotel, as Playboy announced last week. Veteran photographer David Chan will be screening the expected 200 candidates Thursday through Sunday at the Vista Hotel. The Four Seasons, which sees itself as a dignified, residential hotel, wasn't aware Playboy would be interviewing centerfold hopefuls when the reservations were made and was surprised at the number of telephone calls it received when it was reported the interviews would be held there. Robin Brown, resident manager of the Four Seasons, said getting Playboy to move was not based on any moral principle. "It was decided we as a hotel could not accommodate {Playboy's} requests." The Vista, on the other hand, seeing the publicity potential, is doing everything possible to accommodate ... If Frank Sinatra ever gives up singing, he can probably make it in the art world. He sent a serigraph he did titled "Desert Sunset" to last week's Washington Charity Dinner to benefit Nancy Reagan's Drug Abuse Fund, and it was auctioned for $26,000. A group of Hollywood celebrities including William Shatner, Robert Loggia, George Peppard, Pat Boone and Pia Zadora were at the dinner. The winning bidder on the Sinatra work was Tino Barzi, Zadora's manager, who was once Sinatra's manager ...

This is night talker Larry King's big year. The Mutual Radio and CNN talk show host, who is entertaining big contract offers from CNN, ABC-TV and the King World Syndicate, learned yesterday that his book "Tell It to the King," written with Peter Occhiogrosso, will be a Book-of-the-Month Club selection. The book, scheduled for publication in April, will be full of personal stories and anecdotes about famous people King has known and interviewed in his more than 25 years on the air ...

Life magazine is publishing a portion of Michael K. Deaver's upcoming memoirs, titled "Behind the Scenes," in its December issue. A representative of the office of the special counsel, which is investigating Deaver, contacted Time Inc. for an advance look but was told that everyone will have to wait for the Nov. 16 publication date. No exceptions ...