Before we start, I hope someone learned a lesson about the value of backups. Who keeps valuable data in a single location? Unless, of course, these are not *your* data, but I digress
Normally the reason to expose a chip is to get access to its insides in a way that cannot be done by just accessing the bonding pads, which can be done by careful sanding of the outer layers of the epoxy. A prerequisite for that is knowing the layout of the chip. If you have only one copy, *and* you don't know what's inside, *and* you don't know which pads do what, *and* you want a copy of the data, I'd say forget it. Still, if this were the key to a billion dollars, here's what I would do:
First, ask my dentist to take an xray, with the film as close to the back of the chip as possible. Another poster's suggestion to lap the PCB to get to the traces also applies here. In the unlikely event that this is a multi-layer PCB, keep track of exposed inner layers and where they go. I'd definitely want to get rid of all copper before I xray it, for best results.
The xray would also tell me if there is any tamper-resistance built into the package. If there is, I have friends who have done this before and I would go to them for help; without A LOT of prior experience there is no way I would get past even the simplest TR protections, and it would only be worth it if national-security-level interests were at stake.
Unless I got lucky and the epoxy is some inferior material, I would not even attempt to use any organic solvent. Hot WFNA it would be. Now, my parents were chemists, so I learned how to handle things like white fuming nitric acid (WFNA) as a kid, but that stuff is DANGEROUS, and common sense won't save you -- there is nothing commonsensical about the stuff. Then there is the problem of acquiring it and having it shipped to your location without getting on all sorts of watch lists
There can't have been only one of these things made. How did you get it? Why can't you get more?