"May you live in interesting times" I have often heard (and probably repeated) that there is a Chinese curse: "May you live in interesting times."  Is there really such a saying in Chinese? I can't think of one, and can't even think how I would translate it. 

The phrase sounds appealingly enigmatic and understated, and perhaps expresses a preference for stability that might be a Chinese characteristic. You can see why it would resonate with us Brits, particularly in these very 'interesting times' - not just the phrase itself, but that we would think of it as a curse rather than a good wish.
Quote Investigator http://quoteinvestigator.com/2015/12/18/live/ may be helpful here in terms of background. It could not find an earlier citation than a "March 1936 newspaper report in “The Yorkshire Post”:

Sir Austen Chamberlain....said: “It is not so long ago that a member of the Diplomatic Body in London, who had spent some years of his service in China, told me that there was a Chinese curse which took the form of saying, ‘May you live in interesting times.’ There is no doubt that the curse has fallen on us. We move from one crisis to another. We suffer one disturbance and shock after another.