2 Bulb Chandelier not lighting up anymore
Most of the time sockets just go bad.  Though your issue is more likely a lose wire connection probably in the canopy because you did not mention any flicker from the bulbs.

Unfortunately most people have dimmers on chandeliers and dimmers are very sensitive to anything that might go wrong electrically and often go bad.  

So on top of a lose wire connection you could also have a bad dimmer, and not totally ruling out bad sockets. 

So, something as simple as bulbs not working could very well be quite complicated, and not to mention dangerous depending on if the house is wired with outdated wiring and standards.