TL;DR version: Tyrion Lannister is actually the son of the “Mad King” Aerys II Targaryen.
“Prince Aerys … as a youth, he was taken with a certain lady of Casterly Rock, a cousin of Tywin Lannister. When she and Tywin wed, your father drank too much wine at the wedding feast and was heard to say that it was a great pity that the lord’s right to the first night had been abolished. A drunken jape, no more, but Tywin Lannister was not a man to forget such words, or the … the liberties your father took during the bedding.”
-ADWD, Daenerys VII. Spoken by Barristan Selmy.
The “Tyrion is a Targaryen” theory has some textual support, but it requires the theory crafter to stretch the imagination a bit (something most theorists are good at).
Quotes are often just the point-of-view of that specific character, but in the case of Barristan Selmy, it’s relative safe to take the quote at face value. The quote that kicks off this article tells the readers that Aerys II desired Joanna Lannister, and was jealous when she ultimately wed Tywin Lannister. He took “liberties” with her during her wedding night.
What exactly “liberties” means is unknown, but the Tyrion Targaryen theory rests on the presumption that those “liberties” included some baby-making techniques. (It’s easy to come to that conclusion too, because Aerys II complained that the “lord’s right to the first night had been abolished” prior to taking his “liberties.”)
Tyrion’s physical traits
Tyrion’s hair is “so blond it seem[s] white” — a Targaryen-like trait. That tidbit of information came from Jon I in AGOT. In Daenerys I in AGOT, Viserys Targaryens’ hair is described as “silver-blond,” same as Daenerys’.
Tyrion also has mismatched eyes — one green (Lannister) and one black. The black eye does not directly link him to the Targ family. It’s possible, however, that Tyrion’s black eye is actually a deep purple (the same color as Daenerys and several other Targaryens.) It’s not entirely out of the realm of possibility because dark purple eyes appearing black at first has been established in the series.
“His eyes seemed black as he sat outlined against the dying sun, sharpening his steel, but she had looked at them from a closer vantage and she knew that they were purple. Dark purple.”
-AFFC, The Queenmaker.
Black or purple notwithstanding, Tyrion’s mismatched eyes do undoubtedly leave the door open for the “Tyrion is a Targaryen” theory.
Tyrion’s interest in dragons
Tyrion used to dream of having his own dragon, he tells Jon Snow in “A Game of Thrones.” He also used to start fires at Casterly Rock and pretend it was dragonfire. In short, he was fascinated with dragons and what they could do.
This alone does not prove that Tyrion is a Targaryen, but it does lend credence to the theory.
Tywin Lannister’s rejection
And finally, there are also several outright references to Tyrion Lannister potentially not being Tywin Lannister’s son.
“You are your mother’s trueborn son of Lannister.”
“Am I?” the dwarf replied, sardonic. “Do tell my lord father. My mother died birthing me, and he’s never been sure.”
-AGOT, Jon I.
Tywin Lannister also once said to Tyrion: “I cannot prove you are not mine,” and he vehemently refused to give Tyrion Lannister Casterly Rock. The Lannister domain (Casterly Rock) rightfully should have passed to Tyrion because his older brother, Jaime Lannister, forewent his right to Casterly Rock when he became a member of the Kingsguard.
There’s also Tywin Lannister’s dying words to Tyrion: “You…you are no…no son of mine.”
These quotes do not prove anything — one was spoken by Tyrion with his usual wit and the other was spoken by Tywin Lannister as he died — but they do at the very least confirm that Tywin never considered Tyrion his son, a fact Tyrion knew.
Just because Tywin doesn’t believe it doesn’t make it true, but if he’s allowed to doubt then so are we!
So…Tyrion is a Targaryen?
Stitching all of this together and we come to the theory that Tyrion is a Targaryen, at least by half. If so, that qualifies him to be a contender for one of the three heads of the dragon. Daenerys is obviously one of them, and Jon Snow looks like he might be another because of R+L=J. Could Tyrion be the third?
“Even a stunted, twisted, ugly little boy can look down over the world when he’s seated on a dragon’s back.”
-AGOT, Tyrion II.