Princess Alexandra was born on 25 December 1936 at 3 Belgrave Square, London. Her parents were Prince George, Duke of Kent, the fourth son of King George V and Queen Mary, and Princess Marina of Greece and Denmark, a daughter of Prince Nicholas of Greece and Denmark and Grand Duchess Elena Vladimirovna of Russia. She was named after her paternal great-grandmother, Queen Alexandra; her grandmother, Grand Duchess Elena Vladimirovna of Russia; and both of her maternal aunts, Countess Elizabeth of Törring-Jettenbach and Princess Olga of Yugoslavia. She received the name Christabel because she was born on Christmas Day, like her aunt Princess Alice, Duchess of Gloucester. Her birth was the last to have the tradition of having the Home Secretary present to verify the birth of potential heirs to the throne. Sir John Simon was present and was the last to do this.
As a male-line granddaughter of the British monarch, she was styled as a British princess with the prefix Her Royal Highness. At the time of her birth, she was sixth in the line of succession to the British throne, behind her cousins Elizabeth and Margaret, her uncle the Duke of Gloucester, her father the Duke of Kent, and her elder brother Prince Edward. She was born two weeks after the abdication of her uncle King Edward VIII.