Astronaut
The first civilian in space was Valentina Tereshkova aboard Vostok 6 (she also became the first woman in space on that mission).
Tereshkova was only honorarily inducted into the USSR's Air Force, which did not accept female pilots at that time. A month later, Joseph Albert Walker became the first American civilian in space when his X-15 Flight 90 crossed the line, qualifying him by the international definition of spaceflight. Walker had joined the US Army Air Force but was not a member during his flight. 
The first people in space who had never been a member of any country's armed forces were both Konstantin Feoktistov and Boris Yegorov aboard Voskhod 1.
Kalpana Chawla
Her first space mission began on November 17, 1997, as part of the six-astronaut crew that flew the Space Shuttle "Columbia" flight STS-87. Chawla was the first Indian woman to fly in space. She spoke the following words while traveling in the weightlessness of space, "You are just your intelligence." On her first mission, Chawla traveled over 10.4 million miles (16737177.6 km) in 252 orbits of the earth, logging more than 372 hours (15 Days and 12 Hours) in space. During STS-87, she was responsible for deploying the Spartan satellite which malfunctioned, necessitating a spacewalk by Winston Scott and Takao Doi to capture the satellite. A five-month NASA investigation fully exonerated Chawla by identifying errors in software interfaces and the defined procedures of flight crew and ground control. After the completion of STS-87 post-flight activities, Chawla was assigned to technical positions in the astronaut office to work on the space station.