When I installed Google Chrome updates, it broke the Keychain integration. Now, it does not auto-fill any HTML forms (i.e. the saved username/passwords in Keychain.app).
The problem solved itself. I just had to restart Chrome.
Why did that happen? It seems to me that Chrome asked to restart (because it had found new updates), so I restarted it. Then it lost connection with the Keychain. I went to "About" and it showed me to restart again. I did — and everything was resolved.