I've just received my Chopard Mille Miglia back from the watch repairers; it was bought off another collector so I wanted to give it a real good clean. I dismantled the bracelet off the watch splitting it in half and cleaned it in an ultrasonic cleaner using water and soap detergent. Dried it carefully using kitchen paper and then I soaked it in Baby Oil in a bag, massaging the links and working out any dirt.
Cleaned off the oil and polished off any excess using a soft cloth. Reassembled and sized the bracelet and it feels fantastic, smooth and supple. Any excess oil in the pins will work out over time.
Really pleased with the watch, I was going to buy a silicon strap to be traditional, but this bracelet is just so comfortable I may wait a while before moving it a strap.
I will post some pictures at the weekend, the ultrasonic cleaner was only £20 from Lidl if you are in the UK. But many should be available. It cleans straps really well especially my rubber breitlings.