Remove the rust. Pick whatever method floats your boat. Simple car wax will protect any bare metal from further rust. Needs to be reapplied on occasion. Clear coat will work too, but I prefer not to be so evasive.

If your concern is cosmetic, the most expensive option is to rechrome. A cheaper option option is to polish the bare metal, it will be pretty close to looking like the remaining chrome. Buy yourself some 220, 400, 600, 800, 1000, 1500 and 2000 grit sandpaper. Spend the next available 4 hours or so sanding/polishing and Bob's yer uncle.