In the latest season of the History Channel's Vikings, a slave trader brings a Chinese slave among his slaves to Scandinavia, to be purchased by a Viking queen. Could this have been possible during the real Viking Age? How much contact and trade, if any, did the Vikings have with China and the rest of Asia? I am aware that silk managed to make its way to Scandinavia, and that there was a good amount of trade between the Vikings and the Middle East, but I do not know how extensive the contact between Asia and Scandinavia was at the time, especially in regards to East Asia.
I think it's possible but not at all likely. During most of the Viking Age, slaves coming out of Central Asia were traded south, not north. So when the Arab diplomat Ahmed ibn Fadlan met some Norse-speaking slave traders along the Volga River in Russia in 922, they were bringing slaves to sell rather than buying them up to take them back north. It seems like these traders were more interested in obtaining beads and silver, although diverse other objects sometimes made their way back as well.
There is nevertheless a small chance that a Chinese slave might have been traded north as something exotic. There's a few scraps of silk which are likely from China that arrived in Viking Age Scandinavia, but most of the silk that archaeologists have found was probably made in Central Asia or the Byzantine Empire. Very early on in the Viking Age, Scandinavians were able—albeit rarely—to get their hands on items from the further east, such as a famous statue of Buddha from India. But it seems like most of their trade focused on obtaining goods from the Eastern Mediterranean and the Middle East, rather than distant China.