Dreaming about a chimpanzee means intelligence, strength, and power. You may have the feeling that you are not as smart or powerful as you potentially can be. This is because of your own self-doubt when put into new social situations.
The chimpanzee in your dream may also represent someone in your life who has power over you. This person may be a boss or a teacher. You need to be more aware of your surroundings and pay attention to what is going on around you in your waking life when in the presence of these people.