Are bitcoins INHERENTLY fungible? Does each bitcoin has a unique identifier, like currency notes have serial numbers? If so, could you trace a particular bitcoin's ownership chain (ie find the current owner of a particular bitcoin by its identifier)? The answer I'm finding is no:


  There are also specific features of Bitcoin that make this difficult. Transactions put all the input Bitcoins into a big pile which they dole out as outputs. There's no concept of particular output Bitcoins corresponding to particular inputs. Bitcoins don't have a serial number that can be traced through the block chain. So any such tracking rules would be basically arbitrary.
  
  https://bitcoin.stackexchange.com/a/2139/894


Is this accurate?
That is accurate. Let me start explaining how Bitcoins work from the beginning:


Bitcoins are first created when they are mined by solving a block. The first transaction in the block is basically you saying "I'm giving myself 50 Bitcoins to my address A" (plus transaction fees from the block).
When you want to spend Bitcoins, you have to point to one or more transactions that show where you got them from, and say how many Bitcoins you are transferring where. It's like saying "I got Bitcoins at transaction X. I'm sending 20 coins to address B."
The point is that more often than not you don't want to send all the coins you got from the transaction, so you also specify how much change you are sending to another address, usually controlled by yourself: "I got Bitcoins at transaction X. I'm sending 20 coins to address B and 30 coins to address A."
Since all of the above is cryptographically signed, one can be sure nobody can spend coins they don't have (spending more than they have, spending someone else's coins, etc).
To make sure nobody is cheating, everyone is looking at everyone's hands by checking each transaction that comes their way. If you cheat, your transaction does not get forwarded.


I hope that explains the concept of how Bitcoin works in regards to your question. Just to be clear:

"Does each bitcoin has a unique identifier, like currency notes have serial numbers?"

Not like currency (that each bill has a serial number and you can't break them apart), more like bank statements (the identifier identifies the transaction on a certain amount of Bitcoins), but that's still a simplification.

"If so, could you trace a particular bitcoin's ownership chain (ie. find the current owner of a particular bitcoin by its identifier)?"

You can trace the history of transactions on the set of Bitcoins up to who mined them, but not on a particular 1BTC. It's like saying "Alice paid Jill $10. Jill got $20 from Bob. Bob got $50 from the mint."