Lemon juice OR vinegar Steve - both work well mate
If you can fully submerse the part into your chosen fluid
that's all the better - 24 hours usually does the trick.
However if submersing isn't on the cards then soak loads of paper towels / tissues in your lemon / vinegar and wrap it round the rusty bits and cover up with cling film or foil to keep it moist for 24 hours or more
If there's a few stubborn bits afterwards then go for the foil technique - scrunch up, dip in lemon juice / vinegar and rub a dub dub - does the trick and a bit more subtle than flatting it off as the alluminium foil is softer than the chrome so it won't scratch it, but it forms a light abrasive compound as the foil breaks down into little speckles and it's enough to get rid of the rust.
Swivel did a great job on a frame using foil and coke and did a cool thread, and i've done forks with lemon juice and foil and a few seat guts etc. using lemon juice or vinegar submersion with a few threads on results too - have a search and post some pics of yer results
