It will work, that is it will stop the chattering, but it will eventually spread and leave the bearings dry - as all petroleum oils will. You need a synthetic, vegetable, or animal oil, these oils have the property of "staying put" when applied to clean surfaces.
Originally Posted by Cybertrash
Nye or Moebius are two brands to look for online, you'll not find them at any local stores. You'll neeed to clean the mechanism first though, which means disassemble, clean the working surfaces with solvent and reassemble.
Then, apply a very small amount of oil ot the pivots. A steel pen - the sort you dip in ink - is a good way to apply the oil.