The morning after the breach, I mailed security freeze requests to the three credit reporting agencies; and I've gotten the confirmations back from them. The consensus of security experts seems to be that this is Step #1 and that once this is done, credit monitoring services provide very little additional protection (despite what the hyperventilating commercials say).
The postage wasn't cheap--certified mail with return receipts times 3. I'm sending the bill to Anthem. We'll see what happens.