Yes, this is one of the [Jeweler][1]'s abilities. It does cost gold, however, with more gold the higher the level of gem involved.

If you're not interested in getting the item back, you can salvage an item for the same result.

![enter image description here][2]


  [1]: http://us.battle.net/d3/en/artisan/jeweler/
  [2]: https://i.sstatic.net/ut5O8.jpg