Chrome does rust, because it is a metal that readily interacts with moisture and oxygen. Chrome is formed by electroplating a metal with the element chromium, which has greater corrosion resistance than most other metals and increases the durability of the surface.
Although chrome rusts, it is more resilient than other common industrial and consumer metals, which is one of the reasons manufacturers use chrome plating. The rust can be cleaned using aluminum foil, because aluminum has a greater affinity for electrons than chrome plating. Furthermore, when combined with water, the aluminum reacts with chrome to form a high-polish coating, without scratching the chrome surface.