In Heartgold and Soulsilver, after beating Clair and answering all the questions asked by the master of the Dragon Shrine (in the cave) you are gifted a Dratini with Extremespeed.
The procedure is that you have to beat Clair, go into the Dragon Shrine, answer all of the questions asked by the old man correctly. Then you meet Clair in the Gym and go back with an empty slot in the party. The old man will gift you the special Dratini.
Note:If this Dratini is in games prior Gen VI, it has to be male to pass down Extremespeed. However in Gen VI, you can still pas down egg moves from a female parent.