The latest evidence suggests that a desire for mates is the prime motivator behind chimp violence:
Interestingly, human disturbance did not appear to be a factor in the kills. Indeed the community with the most kills—a group at the site of Ngogo in Uganda’s Kibale National Park—had the least human disturbance. Neither was the ratio of males to females in a group a factor. What did appear to be a factor was the number of males in a group: the higher the number of males in a group, the higher the number of kills. Ngogo, the community with the highest rate of kills per year, also had the highest number of adult males. "The number of males is important because the more males there are, the more competition there is for mates in the community," [a researcher] explains.