Of course Keychain will ask for your credentials, but:

1. the extension code runs locally on your browser. It does not rely on an internet connection or a 3rd party service.
2. the provided keys are encrypted and stored locally. They never leave your computer. They are used locally to sign transactions.
3. keychain code is auditable, either on github and even locally after you have installed the extension. It's clear text Javascript.

It's a like a password manager, except that not all password manager code are auditable.
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