In Terminator 2: Judgement day, Cyberdyne made the robot that became the terminators with a chip from a terminator from the future (from the first terminator)

Very late to this thread but it's called a bootstrap paradox. Doctor Who did it with a fez.

The thing with the arm that rob bolton mentioned 18 years ago is something that's always bugged me. It seemed like a clear setup for a sequel, but none of the sequels ever used it.