It's possible he legitimately thinks he did.

Finally watched Season 1's Season Finale episode and here's what I think happened:

Thinking back how Lucille in Arrested Development crashed into a guy on a scooter who she thought was Gob (it really looked like Gov), whilst doing so Michael got knocked out due to the huge rock that was behind him (thanks to Buster) so maybe the same logic could be applied here. I.e, Chip's ex-wife could have switched seats and therefore he'd believe he was the culprit who murdered London's brother.

Maybe Chip's just that good of a forgetful liar that believes his lies to eventually become the truth but I'd be more inclined for the hypothesis that I've brought up.