Chandler told the Eastern Daily Press that the dog started "charging after" Prince William after picking up his scent and started barking at him.
"I had a particularly interesting night when I was walking my dog off the lead around the grounds and he chased after the future king of England," he recalled.
"It was late at night and Prince William was walking towards the garages and the dog picked up his scent and went charging after him. He took it in good jest. He was only young then."
Chandler said it could have gone "horribly wrong" if the future king of England had been bitten, as police dogs are trained to go for the groin area.
"Fortunately the dog did what it was supposed to do, and just stood back and barked at him. It was a memorable night," he recalled.
The royals traditionally gather at the Queen's Norfolk estate for the Christmas holidays.
But the terrifying encounter doesn't seem to have kept William from growing up with a love of dogs.
Last November he shared that he and his family were distraught by the death of their beloved cocker spaniel Lupo.
The family dog was a wedding present from Kate Middleton's brother James. William and Kate shared the heartbreaking news in an Instagram post.
"Very sadly last weekend our dear dog, Lupo, passed away," they wrote.
"He has been at the heart of our family for the past nine years and we will miss him so much."