It's well suspected that the Black Death originated from or near China, however the evidence for something like the huge epidemic like the Black Death in China is complicated for numerous reasons. Three large outbreaks of plagues were recorded in the early to mid 14th century, during the later days of the Mongol Yuan Dynasty rule. Records indicate that some area of China's population were reduced by up to 60%. Of course these numbers can be conflated with other famines, wars and general unrest in China which caused such large population drops in this era (this was an era of huge unrest), but the general population decline in China seemed on par of that with Europe.

Source: http://contagions.wordpress.com/2011/11/26/did-india-and-china-escape-the-black-death/

/u/crazedmongoose already mentioned that there are suspicions it originated in China.

There were also certainly deaths from it in the 13th and 14th centuries. The population was cut in half in a period of just over a hundred years, thought the thoroughness of documentation on cause of death isn't too helpful in knowing which deaths were caused by the plague and which were from famine or war. However there are records of death attributed to the plague, so the only real question is one of ratios.

You may also be interested in this interview on the topic. To quote from that:

Achtman said he owns a plague handbook, published in China in the 1930s, which contains details of "massive" outbreaks of plague in China at roughly the same time as the Black Death was devastating Europe.

Regardless, it's not an easy question to answer definitively thanks to the record available today.

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see also: Sussman GD. 2011. Was the black death in India and China? Bulletin of the History of Medicine