Yes it can.
I was told it couldn't as the Nano sim is actually thinner than a micro sim. I've got one from 3 today ready for next Friday.
I've heard that it can't too, despite the fact that there are nano sim cutters available.
Although what is the difference? 15% thinner? That's literally less than 0.1mm - surely a single swipe of a nail file on the top of it ought to do the trick.
EDIT: Do Three have a nano SIM request page? I presume this SIM would be plug and play on one's existing account and not require re-activating/migration?
Mike