Is it normal for my 7 year old son to have zits?

Not really: Acne is a western disease. Hunter-gatherer cultures are devoid of it. There is substantial evidence for it an a book as been written on the subject by dr loren cordain. Try switching to a more natural diet. Feed your son real food. Nothing form a box or a jar or a can. Eliminate grains, legumes and dairy and see what happens!

No: If he really has acne, you have to make sure he is not exposed to too much male hormone, either from his own body or from outside sources, such as a grandparent's hormone cream. Is he having other signs of puberty, such as a growth spurt, axillary or pubic hair, body odor, etc? I would visit your pediatrician to make sure the lesions are truly acne, and if so, why he has it.

Mild zits are normal: If it bothers him see a dermatologist. If severe the dr will check for abnormal hormones. Does he take any meds or supplements? Diet is important for other reasons but will not help him. I have seen acne all over the world including primitive people who get no modern foods.