Been doing this for years, get SOS pads don't now why but only SOS pads work for this.
Soak them and squeeze all the soap out let them dry use it to get rust off comes off really nicely (use water with it) then use chrome polish to protect it.
On a side note this will also polish aluminum to a shine like a mirror (No water dry) finish (if its rough finish sand with fine sand paper first) take some mothers polish or want ever you like and it will shine!
Other pads just do not do the same job!
All the above work also but this works easy and really makes it shine both chrome and aluminum.
Note: on Chrome use water with it, on Aluminum use it Dry