Pros
'Healthy' company with job security and opportunity for advancement. Due to a large number of employees who will retire within the next 10 years, there's chance for advancement if you take it. In several locations 9/80 is an option--work 80 hours over 9 days (2 weeks). A typical such schedule would be Week 1: M-Th 9 Hours; F 8 Hours. Week 2: M-Th 9 Hours; F off. Though you may be required to work on some off Fridays, it's still a nice benefit as it gives you the chance to take care of activities which must be done during the week (doctors who are not open on weekends etc).
Cons
It is corporate and can move slowly. It can be boring with so many stakeholders needing to buy-in before action can be taken. In such a large company, experiences will vary greatly between different groups and divisions. Similarly, various parts seem to continuously be under consolidation efforts so those parts of the company may be a little less secure. That said, often Chevron will try to retain any talent in such positions if needed or offer nice incentives to leave. San Ramon is nice, but if you have a 'younger' lifestyle is still a big office park with convenient groceries but not much else.