Wow, this thread devolved fast (I like Korean women, too).
I can pretty much only come up with two possibilities:
1. During the medieval period, China splinters into competing states with a balance of power. The competition among coastal Chinese and the Taiwanese, Koreans, and Japanese radically changes China's attitude towards navies. One of these Chinese naval powers settles Sakhalin and Kamchatka, and one day a boat gets blown off course and discovers Alaska. This idea percolates for a couple generations, during which China begins wars of re-unification and has a population explosion. Someone discovers Vancouver Island, and it quickly becomes a million-person settlement. A century later Chinese settlers cross the Rockies, and Chinese Canada takes shape.
2. The Conquest of India goes a little too easy for the British, and they start to pour resources into making the Cantonese lands a colony. The Great Game therefore becomes not over Afghanistan, but over a real prize -- northern China. During the Alt-Great War, the British decide to devolve Imperial Powers away from London to improve lines of communication with the territories. Most territories get some home rule, but the Chinese are too new to be trusted, so the British carve up China and let India, Canada, and Australia share administration of it. Eventually India and Australia become republics, leaving Canada technically in control of China, although for political reasons the Chinese are treated as equals in the Commonwealth.