Chapman was born in Beason, Illinois as the youngest of five. She went to Lincoln College in Lincoln, Illinois, receiving her Associate of Arts degree. She then moved to California and studied animation at the California Institute of the Arts (CalArts). She was a story trainee on the Disney animated film The Little Mermaid. She was one of several key story artists on Disney's Beauty and the Beast, where she worked closely with future Disney director Roger Allers to define many of the key sequences and motifs used in the film. She later served as head of story, the first woman to do so in an animated feature film, for Disney's animated classic The Lion King.
In 1998, she became the first woman to direct an animated feature from a major studio, DreamWorks Animation's The Prince of Egypt.
She co-directed the 2012Disney/Pixar film Brave, becoming the first woman to win the Academy Award for Best Animated Feature. Chapman's daughter Emma was the inspiration for Merida in Brave.