"How are you doing?" asked Rep. Claude Pepper (D-Fla.), shaking the hand of the world's second-strongest chess player.

"I am doing well," answered Victor Korchnoi, "but my family is doing badly."

Korchnoi, a perennial contender for the world chess championship, has been a citizen of the world since defecting from the Soviet Union in 1976. After years of temporary residence in one country after another, he is considering a permanent residence in the United States--probably on the Upper East Side of Manhattan, according to friends. Yesterday, on a whirlwind visit to Washington, he put chess aside to talk to congressmen about the plight of his family, whom he calls "hostages" of the Soviet Union.

"My son is in a prison camp," he told Pepper, "on charges of avoiding military service but really for my crime of leaving the Soviet Union."

"He will be one of your constituents," Lev Alburt, another Soviet defector and chess grandmaster, was telling Rep. Bill Green (R-N.Y.), whose district currently runs down the East Side from 90th Street past Greenwich Village. "We'll see," said Green, "after they finish revising the boundaries." But he promised to do what he can for Korchnoi, who at present cannot vote in the United States or anywhere else.

At a reception in the Rayburn House Office Building, hosted by the Union of Councils for Soviet Jews, the guest list included more than a dozen congressmen, Jewish activists and a scattering of chess players and fans, including Alburt and Bruce Pandolfini, a staff member of Chess Life and Review magazine. The buffet was good and the drinks flowed freely, but there was an underlying concern for Jews in the Soviet Union, whose emigration visas have been drastically curtailed in recent years.

"I have a terrible fear," UCSJ president Lynn Singer was telling a congressman, "that if the door closes, it will be a minimum of a decade before it opens again." In the last 11 years, she said, 270,000 Jews have been allowed to emigrate from the Soviet Union, "but we sent in over 600,000 invitations from Israel. Where are the others? We know of at least 10,000 families that have been refused for spurious reasons. They talk about knowledge of state secrets! The lady is sweeping streets in Moscow; she knows how many strokes it takes to cover a street!"

Korchnoi and the UCSJ claim that the Soviet government has promised to release Korchnoi's family when his son, Igor, finishes his prison term on May 13. "We have only the next few weeks to remind the Soviets of this commitment," Singer said. "It is necessary," added Korchnoi, "to remind them that they have promised something and not let them get away with anything."

Many of the congressmen welcomed the appeal. "We already communicate with the Russians," said Rep. William Brodhead (D-Mich.). "We write not only to Brezhnev but to local officials who make some basic decisions. We want the Soviets to know that Americans believe respect for human rights is essential to detente."