Pros
Chevron is a great place to work if you're an engineer. Pay is great, benefits are awesome, the 9/80 schedule provides a lot of flexibility (every other Friday off, but work 9 hours during the week and 8 hours on your Friday on). They treat everyone fairly and are very big on diversity and safety. They are also strong proponents of work/life balance. You have just about an endless amount of sick time and entry level employees start out with 2 weeks of paid vacation, increasing by 1 week every 5 years.
Cons
I work in IT and while it is great company, they do not necessarily view IT employees as valued. In fact, IT employees are referred to as "non-technical" because only the engineering jobs are the "technical" jobs. Chevron pays well for IT jobs if you're freshly out of college, but once you have a few years of experience under your belt, it might be worthwhile to go somewhere else and get a bump in pay.