The Passport supports Android 4.3 Jelly Bean apps. To run Chrome, you typically need to source an older APK file compatible with this version.
To get Chrome running on your Passport, follow these general steps: google chrome for blackberry passport
based on Android 4.3 Jelly Bean, it can run older Android APKs. However, you cannot simply go to the "App World" to find it. How to Install Google Chrome The Passport supports Android 4
Tabs & multitasking: Good tab handling and quick switching; tab thumbnails are usable but the Passport’s screen limits how many you can comfortably view at once. However, you cannot simply go to the "App World" to find it
Unfortunately, Google Chrome was not officially available on the BlackBerry Passport through the BlackBerry World store or any other means. BlackBerry's own browser, BlackBerry Browser, was the default browser pre-installed on the device. However, users could access the internet and browse websites using this browser.