Do you need a license to pierce ears?

No, you don't. All of those chicks in Claire's that use guns to pierce ears only have to read a book that takes about 15 mins to complete. Shows how experienced they are. If you visit the Association of Professional Piercers'(APP) website they have an entire section on how to become licensed with them. The APP is highly reputable and most people will only go to APP certified shops/piercers.

(The APP is not a licensing or certifying body, they function more like a guild or union, for lack of a better analogy.)