Correct me if I'm wrong, but the original grilles are not technically chrome, they're anodized aluminum. At a glance, I don't see any posts for how to "polish" these without removing the finish. You might try diluted simple green and a soft cloth. Some low abrasive paint polish may work well.
I found this on-line. Little confusing however. The title reads for anodized aluminum, but the description says for "uncoated" aluminum.....WTH?
Amazon.com: Autosol Anodized Aluminum Polish 75ml...