Chapman was born in Kangaroo Island. One of seven children, Chapman attended the Kangaroo Island Parndana Area School, and following the death of her mother at age 12, she later attended Pembroke School in Adelaide. She studied a law degree at the University of Adelaide and graduated in 1979 as a barrister.
Chapman's father, Ted, was a member of the Liberal and Country League and then the South Australian Division of the Liberal Party of Australia in the South Australian House of Assembly. A Liberal moderate, Ted was a member of the Steele Hall-led Liberal Movement faction in the 1970s and Agriculture Minister in the David Tonkin government. As a young girl, Chapman assisted her father in Liberal campaigns for office.
At one stage the Liberal Party state president, Chapman attempted to win Liberal preselection for the federal division of Barker in 1998. Her husband, David, died in 2001 and she moved from Wayville to Tusmore with her two children. She again tried to win preselection, this time for the safest Liberal seat in the metropolitan area, Bragg, located in Adelaide's wealthy eastern suburbs. When sitting member Graham Ingerson resigned, Chapman contested preselection against Liberal minister Michael Armitage, who was seeking to move from his marginal seat of Adelaide. Chapman easily gained preselection and retained Bragg with a slight 0.4-point two-party swing at the 2002 state election when the Liberals lost government. She was soon touted by some quarters, within her party and in the media, as a future Liberal leader. In other quarters, however, Chapman was seen as a continuation of the Chapman/Brown and Evans/Olsen divisions.
Immediately upon her election to parliament, she attained the shadow portfolios of Education and Children's Services. After the Liberals were defeated at the 2006 election landslide where Chapman suffered a substantial 6.8-point two-party swing, Chapman was elected to the deputy leadership of the party in an unexpected joint ticket with factional rival Iain Evans. Strong backing was received from moderate faction bosses: former Premier Dean Brown and federal Sturt MP Christopher Pyne. Pyne has long been a close factional ally of Chapman.
Liberal leader Martin Hamilton-Smith called a leadership and deputy leadership spill for 4 July 2009. Chapman ran against Hamilton-Smith for the leadership, but received only 10 votes, against Hamilton-Smith's 11, with Evans abstaining. Isobel Redmond was elected to the deputy leadership to replace Chapman. Hamilton-Smith called another leadership spill to take place on 8 July 2009, in an attempt to gain a more decisive mandate, but two days prior to the spill, he announced he would not run. Chapman again ran for the leadership but received only 9 votes, against Redmond's 13. Steven Griffiths was elected deputy leader 8 votes to 6 for Mitch Williams.
Despite having attempted to previously oust Hamilton-Smith as leader and having attempted to later defeat Redmond in a leadership ballot, Chapman voted for Hamilton-Smith in his successful bid as deputy leader on 31 March 2010 in a vote held after the third consecutive Liberal loss at the 2010 election where Chapman gained a substantial 9.1-point two-party swing. Voting for Hamilton-Smith as deputy meant not voting for Evans. Chapman drew headlines in the last week before the 2010 election for not being willing to publicly refuse challenging Redmond for the leadership and faced accusations, particularly by Hamilton-Smith, of derailing the Liberal campaign, with "Chapman Could Challenge" posters hung beneath many of the Liberal "Redmond is Ready" posters.
Chapman was reappointed deputy opposition leader on 4 February 2013, and chose to announce she would rule out challenging new leader Steven Marshall.
Upon the fourth consecutive Liberal loss at the 2014 election, Chapman suffered a 1.5-point two-party swing but still finished with a 68.7 percent two-party vote in her very safe Liberal seat of Bragg.
One of her children is Channel 7 reporter Alex Hart