There are two Keychains relevant to each individual user account. There is one referred to as the 'Login' Keychain which is located at ~/Library/Keychains/login.keychain and there is a second one referred to as the 'Local Items' Keychain which is located at ~/Library/Keychains/00000000-0000-0000-0000-000000000000/ and in this folder are several files in particular keychain-2.db which is an SQL Lite database file.
The 'Local Items' keychain as should be obvious from the above is in a completely different format to the Login Keychain. The folder it is in is a long hexadecimal number which actually matches the unique UUID number of the Mac you are using. This number can be found via System Profiler.
As an aside the Local Items keychain seems only to be used by Apple software e.g. Mail, Contacts, Calendar and Safari. It was 'invented' to add the ability to sync the keychain via iCloud and even if you don't use iCloud it is still created and used. It is a huge pain in the neck if your using Network Home Directories as due to the fact it is in a uniquely named folder based on the unique UUID of the Mac your using it prevents doing 'hot design' and even worse due to it being an SQL Lite database and being accessed via a file server - if your using network home directories has a nasty habit of regularly getting corrupted. 😠 These are issues Apple have been aware of for years but still have not fixed even in Sierra. 😠 If your using a laptop with a local account - something Apple seem to assume is the only setup now used by the customers then these issues will not really affect you.
Getting back to restoring your keychains you would need to navigate to your ~/Library/Keychains folder and then enter Time Machine. To see your Library folder you need to go through some extra steps as some time ago Apple decided to 'hide' it to prevent users accidentally messing it up. See this article for two methods to get to your Library folder.
http://osxdaily.com/2013/10/28/show-user-library-folder-os-x-mavericks/
You can chose to restore just the login keychain but this as mentioned does not contain your Mail etc. passwords, or restore the Local Items keychain or both. When you restore them it will overwrite the new empty version. You should immediately after restoring the old ones logout and then back in so that it recognises the change and loads the restored copies.
