Pros
Coming from another oil company, I have had an opportunity to compare/contrast the company culture and work experience.....and Chevron comes ahead, hands down. I enjoyed my previous company and did well there, but Chevron's commitment to their employees and stockholders while maintaining corporate integrity has been inspirational. Like others mentioned, there are lots of opportunities to move up within Chevron if you are a strong performer, especially if you are mobile. I have heard from many people that once you are in, it's hard to get fired unless you are a really poor performer - they are more apt to "reshuffle" you than let you go. That, unfortunately, does lead to some people still with the company that should be eliminated. Overall the company employs a high caliber of talent - people who enjoy their work and are extremely loyal to the company. They love the company so much they end up hiring their relatives and friends - there are a high percentage of people I have met that are somehow related to another employee (hence the nepotism mentioned in another post).
Cons
Salary pay is very competitive compared to other oil companies, although annual pay increases are on the modest side. While I don't 100% agree with the "good ol' boy" network comments others have made, I do agree that management typically promotes those that have qualities and characteristics similar to them. You don't need to be in the "in crowd" to get promoted, but you should have a personality and style similar to those higher ups. It is also actively up to the employee to determine their future - the company expects people to network if they want a position, it doesn't get handed to you. This is where some "schmoozers" get ahead of the quiet bees.