Depends on the method used to print. If you use selective laser sintering (which is what Shapeways uses), what you do is keep on adding layers of a fine powder

Depends on the method used to print. If you use selective laser sintering (which is what Shapeways uses), what you do is keep on adding layers of a fine powder, then us a laser to fuse them together in the places where you want your object. The powder supports the object, so things like a chain are entirely possible to print. When you're done, you drain the powder away and have your completed object (which you may then do further finishing on like sanding or painting). Other 3D printing methods like extrusion may be able to do so, if they have two nozzles and can print both the final material and some supporting material that could be melted or dissolved away.