Since you are not using the Play Store, you must allow installation from outside sources.
To run Chrome on Android 4.0.4, you must download a legacy version. Last Supported Version: The final official release for Android 4.0.4 was Chrome 42.0.2311.111 , released in April 2015. Where to Download: Download Chrome Browser Apk For Android 4.0 4
: Go to Settings > Security and check the box for "Unknown Sources" to allow installations from outside the Play Store. Since you are not using the Play Store,