The stateswoman who is a concert level pianist was allowed to use a music room at the palace after expressing a wish to play for the Queen before leaving office at the end of the Bush administration in January.
The Queen listened to part of the performance, and afterward presented Miss Rice with an audio recording of the recital as a gift.
Miss Rice started playing the piano as a child and planned a career in music, originally enrolling at university to study the subject before switching to political science. At 15 she performed Mozart's Piano Concerto in D minor with the Denver Symphony Orchestra, as a prize for winning a student competition.
She was taught the instrument by her mother, who was a music teacher, and regularly performs private chamber music recitals with four friends, leading to her be described as the world's most prominent amateur musician.
Miss Rice was visiting London before heading for Brussels to attend a meeting of Nato leaders. Earlier in the day, she met Gordon Brown and Mr Miliband.--Telegraph