Why is the Unicorn on the Scottish Coat of Arms?

In 1423 James I was in England at Henry VI’s pleasure. He was out walking one day when he saw Joan Beaufort, daughter of the Earl of Somerset stroking a Unicorn.

Now Unicorns only make themselves known to those who are pure and virtuous, so he knew he was onto a good thing here. He sneaked up and slipped a royal coronet over the Unicorn’s head and slipped a chain on it. When he was released (for a ransom of £40,000) he married Joan and the unicorn was incorporated on the Scottish coat of arms.

Source - Traditions of Edinburgh by Robert Chambers

Link to the Undiscovered Scotland site.