At first glance I believe it is the Order of the Cloud and Banner, 4th Grade.

I think it is a medal for the "Order of the Cloud and Banner", seen here:

http://en.wikipedia.org/wiki/Order_of_the_Cloud_and_Banner

Which is awarded by the Republic of China, better known after the war as Taiwan. So there is no connection to the current government of China.

There's a brief analysis of why people received this decoration here: http://flying-tiger-ace.tripod.com/id51.htm

I don't know what branch of the military your grandfather was in, knowing that would probably help a great deal to get down to the details as to why he received it. But it is clear that a number of Americans received this decoration... I assume your grandfather was in the US military?

edit: and if I'm reading http://www.medals.org.uk/taiwan/taiwan009.htm correctly then I would agree with Kitarn that this is 4th grade.