What’s the theory? R+L=J

(For the uninitiated, this stands for Rhaegar + Lyanna = Jon, i.e. Jon Snow is not Ned Stark’s illegitimate son at all, but the son of Rhaegar Targaryen and Lyanna Stark.)

Prove it! We know that Rhaegar absconded with Lyanna (willingly or otherwise) and they were together for some months before Rhaegar’s death at the Trident. We know that Lyanna was sent to the Tower of Joy with half the Kingsguard protecting/guarding her. If she was taken unwillingly they might have been keeping her there, but if she went willingly, that doesn’t really make sense – the Kingsguard should be with either the King or the Crown Prince, not a woman who was active and not afraid to fight herself – unless she was heavily pregnant with the Crown Prince’s son. It’s possible that Rhaegar raped Lyanna as Robert believed, but the theory makes even more sense if we assume she willingly ran off with him, since everyone but Robert, including Ned, thinks of Rhaegar as a noble, generally good Crown Prince.

Ned Stark remembers finding Lyanna in ‘a bed of blood’, a description used elsewhere in the series to refer to childbirth. Ned made a promise to her on her deathbed that has cost him a lot of sleep over the years. Considering Robert’s satisfaction with the murder of Rhaegar’s children by Elia and the danger posed by any Targaryen heir (illegitimate children can be legitimised, like Ramsey Bolton, and there is some speculation that Rhaegar and Lyanna might have got married, since several earlier Targaryens had multiple wives), it would make sense if Ned’s promise were to protect Lyanna’s son. He did so by claiming the baby as his own son instead, something which cost him a lot because it hurt his new wife Catelyn and compromised his reputation for unimpeachable honour.

Jon is definitely a Stark – genetics is much simpler in Westeros than in reality and he looks far too much like a Stark not to be related to them. However, he looks like Arya, who in turn looks like Lyanna, so while he is ‘of Ned’s blood’, he isn’t necessarily his son. It’s also worth noting that in episode two of the TV series, Ned tells Jon that next time he sees him, they’ll talk about his mother. Ned expects that when they see each other again, Jon will be a sworn member of the Night’s Watch, meaning that, like Maester Aemon, he can never claim any birthright or inheritance from whoever his biological parents might be. It’s possible that Ned intended to tell him the truth once he had removed himself more firmly from any claim to the throne.

Finally, in the House of the Undying, Daenerys sees a blue rose growing out of a wall of ice. The wall of ice seems pretty easy to place as The Wall, as Lyanna Stark was fond of blue roses – so the implication is that Dany is seeing a vision relating to her biological nephew, Jon.