Google has released an update to Chrome for iOS, bringing it up to Chrome 66 and bringing the ability to export your passwords from the mobile browser. The update is already in the App Store and if you have Chrome for iOS installed on your iPhone or iPad, you likely already have received the update.
The new build brings the mobile browser up to speed with the Android version as well as the desktop versions by basing it on Chrome 66. The ability to export passwords was actually in the iOS version in Chrome 65 but it had to be enabled through the changing of a flag in the browser. In this update, it is fully supported and no flag changes are required.
The new export feature is found in Settings under Passwords. You will see your entire list of passwords saved in Chrome on this page. Scroll down to the bottom of the page and you will now see an export option. Your passwords will be saved as a .CSV file which you can then save to your cloud storage or locally.
To be clear, and Google points this out, anyone with access to the .CSV file will be able to see your passwords as it is not encrypted. Be sure you only export your passwords if you absolutely need to do so and to keep that file securely stored.