Hi Dan,
Solvol usually does the job for me, takes a while but you don't risk damaging the chrome that way (too much, based on the idea that anything abrasive will cause it some problems if used often enough, hard enough, long enough)?
You know it is working as the clean cloth gets stained from the oil, and the spots or runs start to get smaller, usually the edges start to reduce in size or the thick raised droplet (if that is what you've got) start to reduce in height at the high point.
You could try it with a plastic non-scratch pan cleaner - I get mine from Tesco (but other brands available!!!!). They do two types so make sure you get the non-scouring one, not the Scotch-Brite range of products.
Using Solvol and a non-scratch (instead of a rag) will, I am sure, do the trick - it'll just take some time and effort.
Best of luck.
Stuart