I picked up a copy of the Biblical Archaeology magazine for a recent trip. In there, I stumbled upon this in an editorial. You will need a subscription to get the link to work.
In the article discussing who owns artifacts, the culture that produced them, or the country which currently owns the land the artifacts were discovered on, the editor says that the broken pieces of the original tablets with the 10 commandments were found back in 1969!
<tangent>Why is this not well known? Holy hidden treasure, this is big.</tangent>
I just happened to stumble upon that little bit of information. I searched online, but either my search skills are sub-par (probably) or there is nothing about this find on the internet.