Are there chips encoded with fixed 8bit values?
Usually when we need something like that, an EEPROM is used. It's convenient to be able to change the numbers at will then lock them. Some EEPROMs are available pre-programmed with unique numbers such as MAC addresses. 

For a few bits, these things are still available (called DIP shunts). 



To program them to any of the 255 other possible combinations, you poke through the hole and break the connection as so: 



Of course you could always use a DIP switch, but that would be easier to change.