I applied and interviewed through my university. Two young Chevron representatives who worked within the area I applied for conducted the interview. The questions were entirely behavioral and not difficult. They especially look for leadership skills and personality in addition to your credentials. At the end they asked if I had other offers, and to let them know if I had to accept by a certain date. I did, and notified them. I received an offer within two weeks.
Since it is such a large company, the process was a bit impersonal and I struggled figuring out who to contact. I was not able to receive a detailed explanation of what I would be doing during the internship.