I came into Chevron from outside. From what I've seen, I don't think many Chevron employees will be successful in the open job market. A typical Chevron employee spends 1/3 to 1/2 of his or her time on corporate bullshit, instead of real work that matters and adds value. The horizons program is deeply flawed, nobody outside Chevron is going to care about what training courses you completed, what meetings you planned/attended, or how many e-mails you answered. Employers want problem-solvers, not process-followers.
What you need to focus on, right now, is how you are going to document your work experience and knowledge to a potential future employer during the interview process. Polish your resume, ask people that you trust for references, and put together a powerpoint that you can present in a future interview. Do it now, don't wait until you are left standing.