How did chief get Cortana back without having her chip in the 5th mission. Chief uploads Cortana and the the Librarian abducts her. While Chief is looking for her he doesn’t pick up the chip and when he speaks to the Librarian Cortana shows up in another podium and somehow gets transferred back to chief without the chip.
Take a look http://www.youtube.com/watch?v=PK-Ts5CcSLI
at 44:40 and 50:45