The band, who are playing at London's Hyde Park festival, say some of their footage from their early days together was taken.
They made the revelation as they prepare to release their new documentary Talihina Sky, which includes interviews with the band as well as archive footage.
Nathan Followill said to BBC Newsbeat: 'Whoever's got the tapes really don't know what they got.'
Caleb Followill added: 'There was quite a bit we weren't able to show [in the documentary] because we had our car broken into after we were making the first record.
'We'd documented every bit of it and they stole all the footage.'