Travis is right, I even read figures as high as 60 000 Canadians serving in Vietnam.
The figure I read was 13,000. Will have to do some digging.
Interestingly a bunch of Canadians were drafted as they were working as foreign nationals and eligible for the draft. You had a choice, serve or never return to the US (until the amnesty that is). Around 3k chose to serve after being drafted. The other 10k were cross-border volunteers.