The Soyuz TMA-01M was launched at the scheduled time of 5:10 a.m. (2310 GMT) from the Baikonur cosmodrome in the vast steppe of southern Kazakhstan.
Scott Kelly and Russia's Alexander Kaleri and Oleg Skripochka are due to reach the orbiting laboratory in two days to begin their five-month mission. They will join two U.S. astronauts and a Russian cosmonaut who have been at the station since June.
Chapman, who has avoided the public and the press since being deported from the United States in July, appeared at the farewell ceremony for the space crew. She told an Associated Press reporter that she had "just arrived" and refused to answer any questions.
She then walked hastily to a guarded guest house near the launch pad accompanied by a burly man who blocked her from reporters.
An official with Russia's space agency, speaking on condition of anonymity, said Chapman was at Baikonur as an adviser to the president of FondServisBank. The bank works with space industry companies and was handing out awards, the official said.
Chapman was one of 10 Russian spies deported from the United States. Her sultry photos gleaned from social-networking sites made her a tabloid sensation.
Since returning to Russia she has kept a low profile. Last week, a trendy Moscow night club invited the media to a party to meet "the head heroine of the spy scandal of the year, the Russian Mata Hari Anna Chapman." But she did not show.
Kelly and the two Russians on their way to the International Space Station are flying in Russia's first all-digital Soyuz TMA-01M.
The overhauled Soyuz will allow a doubling of the launch rate of Soyuz spaceships, which will help maintain a crew of six aboard the space station when the NASA shuttle fleet is retired.
Kelly, a New Jersey native, will be joined at the space station by his twin brother Mark, another NASA astronaut who will fly a shuttle mission in February. The Endeavor that will bring Mark Kelly to space is the next-to-last U.S. shuttle before NASA wraps up 30 years of shuttle flight.
The International Space Station celebrates its 10th anniversary on Nov. 20. The mammoth station consists of 10 modules built by the United States, Russia, Canada, Japan and the 18-nation European Space Agency.