Chopra was born in Jamshedpur, Jharkhand to Ashok Chopra and Madhu Akhauri, both physicians by profession. Chopra spent her childhood in Bareilly, Uttar Pradesh; Newton, Massachusetts; and Cedar Rapids, Iowa. Her father was in the army and thus her family moved quite frequently. Her father hailed from a family of Punjabi origin, settled in Bareilly and her mother comes from a family settled in Jamshedpur. She also has a brother, Siddharth, who is seven years younger than she is.
Chopra studied at La Martiniere Girls School in Lucknow as a young girl. She subsequently re-located to the U.S. where she studied in Newton South High School in Newton, Massachusetts and then in Jhon F. Kennedy High School in Cedar Rapids, Iowa. She returned to India and finished her high school at Army School in Bareilly. She began college at Jai Hind College in Mumbai, but left after winning the Miss World pageant.