I was in an RF anechoic chamber once, at an Underwriters Laboratory facility in Rahleigh.
It may not have been as quiet as a sonically anechoic chamber, but it was very quiet. Similar construction, but intended for a electromagnetic absorption, and maybe not quite as large.
And have been in caves, which may share similar level of quiet, at least when no sounds are being locally generated. It's hard to say, when all you hear is nothing.