Where exactly is the Google Chrome sync passphrase?
I have an entry called GoogleContactSyncService which is an application password, then I have a Google Chrome Sync Passphrase which is stored as a secure note, but I may have added that. Try the former.

If this isn't it, then it is likely an application specific password. Go to your Google Account, revoke the prior Authorization and then generate a new password. If the one I said above isn't it then I have a feeling that what happens is that when you enter the passphrase it generates a much larger authorization token from it which is stored in keychain. The app password doesn't get stored.

Update

I think that you needed to record it, which is likely why I have a secure note in my keychain where I stored the passphrase when I set it up. If you didn't do something similar, or write it down when you set up, then you won't have it. 

What is on your computer is the encryption key that is generated by a key derivation function (password hash). Basically you enter the passphrase and the function creates a large, pseudorandom private key with the passphrase as the seed for the random function, though Chrome's algorithm is likely more complex than that. Enter the same passphrase into the function and the resulting key will return the same key. However you shouldn't be able to go in reverse and use the key to generate the passphrase.

There is a possibility that if you didn't choose to use a different passphrase that it will be your Google account login password. If you have change your Google account password, try the older passwords to see if that was the one used as the passphrase. If you generated an app specific password and you didn't record it then the synced data is locked. You will have to reset and start from scratch.