After one of the episodes with Jack’s dad in Australia arguing with a young blonde woman there was wide speculation that Jack and Claire were related. In an interview with USAToday, Locke confirmed this theory when he was asked:
Q: One of the biggest flashback mysteries was Christian Shepherd’s (Jack’s father) argument with a blond Australian woman in the episode Two for the Road. Christian wanted to see his “daughter” and the woman would not let him in her house. Wild speculation followed and most people believe Claire could be Jack’s half sister. Will there be any more information revealed this season? Conor Hogan
Which his response was:
A: “I have no doubt that Claire is Jack’s half sister. Trust me the people that are creating this story do not throw (stuff) like that around lightly. He knocked on a door and a woman said, ‘You’re not being a part of her life. I want you out of her life.’ People who pay really close attention to the show know that that woman is Claire’s mother. And that’s why Christian ended up going to Australia. That was put there for people to think that specific thing and so therefore I think that we will find out that that is absolutely true and in fact that her child is Jack’s nephew. In my mind, this is a slam dunk! To find out they are actually related by the same father and they don’t have any idea after all their moments during the birth of the baby, is really great stuff!”
Terry O’Quinn (Locke)
Here is the rest of the interview which doesn’t offer too much to us.