27 September 2014 Last updated at 07:31 
“Marc and I are full of love, awe and gratitude as we celebrate the birth of our daughter, Charlotte Clinton Mezvinsky,” Ms Clinton tweeted.
Ms Clinton, 34, married Marc Mezvinsky in 2010, and announced her pregnancy in April 2014.
The baby arrives as Hillary Clinton considers a presidential bid in 2016.
She is seen as the leading Democratic contender for nomination to succeed President Barack Obama, and has said that she will make a decision on whether to run from around the beginning of 2015.
Bill Clinton served as the 42nd US president, from January 1993 to January 2001.
The former first daughter has often been tipped to follow her parents into politics.
Chelsea Clinton, educated at Stanford, Columbia and Oxford Universities, runs the Clinton Foundation with her parents. Her husband Marc Mezvinsky is an investment banker.
Ms Clinton stepped down from a $600,000 (£370,000) a year position as NBC special correspondent in August to concentrate on her pregnancy, motherhood and philanthropic work.
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Chelsea Clinton gives birth to girl
