If you are bothered that much and don't have a lot to lose I would leave as soon as possible. Once the layoffs start there will be more competition on the streets for jobs. You will have Anadarko and other ex-employees from companies out looking for some of the same jobs.
This poster makes a great point. In a month, two, or whenever Chevron decides to start cutting, job market will be flooded with people with same skills and experience. Deciding to leave now could make a difference between being able to find a new job right away and being stuck unemployed for who knows how long.