Seems unlikely based on recent experience
They're only achieving a launch rate of 1 manned mission every 1-2 years. While it's true that the Chinese don't have to invent all of the things we needed to land on the moon, they do need to create a cadre of skilled personnel and flight test a lot of hardware before being ready for a moon mission. At the current launch rate, they'll only have flown less than 10 manned missions by 2017. I'm not saying it'd be impossible, just a bit of a stretch. Now, if they devote the resources and step up the launch rate substancially, it's quite possible they could do it.