Christine was born on 9 September 1944 in Burton-on-Trent, Staffordshire, England and brought up in Edinburgh, attending Boroughmuir High School. She went on to attain an MA from the University of Edinburgh in 1965 and subsequently gained her Diploma in Education from Moray House College of Education in 1966. After graduating, Grahame worked as an English teacher in a number of secondary schools. After a period as a housewife, she returned to Edinburgh University as a mature student where she earned a law degree in 1984 and a Diploma in Legal Practice in 1985, subsequently practicing as a solicitor at a number of law firms until her election as an MSP in 1999.
Grahame joined the Scottish National Party in 1970 and has been an MSP since the Scottish Parliament was established in 1999. In that 1999 Scottish Parliament election she fought Tweeddale, Ettrick and Lauderdale. Although she finished second, her position on the SNP regional list took her to Holyrood. She contested Tweeddale, Ettrick and Lauderdale at both the 2003 and 2007 elections, coming within 1,000 votes of victory on both occasions and being returned once more as a regional MSP for the South of Scotland.
In the 2011 Scottish Parliamentary election, Grahame won the redrawn seat of Midlothian South, Tweeddale and Lauderdale, defeating former Liberal Democrat finance spokesman Jeremy Purvis (now Baron Purvis of Tweed). She held the seat in the 2016 Scottish Parliamentary election, increasing her share of the vote to 45.1%. She is currently seeking re-election in the same seat in the 2021 elections.
In the 5th session of parliament, between 2016 and 2021, Christine served as the Deputy Presiding Officer and also chaired the Cross Party Group on Animal Welfare.