Since they haven’t tested humans yet, I’m not sure I buy it but since I eat broccoli all the time (it’s practically the only vegetable I can get my kids to eat) I’d be happy if it were true:

Eat your broccoli! That’s the advice from UCLA researchers who have found that a chemical in broccoli and other cruciferous vegetables may hold a key to restoring the body’s immunity, which declines as we age.

Published in the online edition of the Journal of Allergy and Clinical Immunology, the study findings show that sulforaphane, a chemical in broccoli, switches on a set of antioxidant genes and enzymes in specific immune cells, which then combat the injurious effects of molecules known as free radicals that can damage cells and lead to disease.
Free radicals are byproducts of normal body processes, such as the metabolic conversion of food into energy, and can also enter the body through small particles present in polluted air. A supercharged form of oxygen, these molecules can cause oxidative tissue damage, leading to disease — for example, triggering the inflammation process that causes clogged arteries. Oxidative damage to body tissues and organs is thought to be one of the major causes of aging.