To keep your data private within the app, you can enable a password. Touch ID for MacBook Pro (2016 and later) is now available in version 2.6.
This does not encrypt your data on the hard drive. If you are using a shared computer, we recommend using separate user profiles for the computer and enabling FileVault to encrypt the hard drive data.
Click Day One > Preferences (in the file menu) > Security.
The next time you open Day One, or after the indicated minutes of inactivity, the password prompt will appear.
For MacBooks with Touch Bar, here is the view with Touch ID enabled:
Resetting the app-locking passcode