Yes they are made of bamboo. The Chinese letter for chopsticks is a combination of 'fast' and 'bamboo'.

I also highly doubt america produces more than a fraction of those made in asia. Is bamboo even growing in north america?

Bamboo can grow in North America but I don't believe it's native, I imagine it's largely grown as an ornamental, possibly with some farmed?

There was a company in Americus, GA that was exporting millions of chopsticks to China, but it bounced a $1M+ check and went into receivership. I've not seen anything about it recently: http://www.npr.org/2011/07/27/138761682/georgia-company-expo...