Pros
Chevron respects their employees and empowers us to create the career we want in the long term. It's a company that wants employees to work here for 30+ year careers and tries very hard to place you in opportunities where you will be successful. When there are re-orgs, the company works hard to prevent mass layoffs and takes careful steps to ensure that as many people are found jobs rather than kicking them to the curb as some other companies do. As a project manager, I find their project methodology, CPDEP, to be one of the best. Most project professionals I work with utilize this process as it's intended; a framework for successful projects. We are well-paid and have a great work/life balance.
Cons
Depending on the project or department you are in, it can get quite 'political.' The fact that the company is reluctant to fire people is a double-edged sword. In other words, there are some managers who don't practice the collaborative "Chevron Way" yet get to keep their positions. The PMP process (internal ranking of employees) could stand to show more visibility in the process. I suspect it's more "political" then they make it out to be.