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The Omaha project is a top-secret military operation. Omaha was first mentioned in Chuck Versus the Alma Mater where Stanford University professor George Fleming explains to Bryce that the CIA needs Chuck for the Omaha project:


Bryce and Chuck at Stanford

Bryce: Chuck Bartowski? He never got your message.
Fleming: What are you talking about?
Bryce: You put Chuck on the CIA recruitment track.
Fleming: It's not up to me, Bryce. They want him for the Omaha project.
Bryce: That's a military operation. They'll turn Chuck....
Fleming: I'm required to send all the top test results to the agency.
Bryce: I want my friend out of this.

Another possible reference is made in Chuck Versus the Nemesis where Bryce tells Sarah "We will always have Omaha" (another Casablanca reference).

There is a possibility that the Omaha Project was somehow connected with the Intersect since Professor Fleming says that Chuck is a perfect candidate because the "Keywords in his essay responses correlated with 98% of the subliminal images in the exam" and he emphasized that "the agency is not going to let go of a recruit this promising" because of the amount of information Chuck can retain. This would also explain further why Bryce chose Chuck as the recipient of the Intersect.