Reinstall Google Chrome on iPod Touch 4th generation
Yes, you can do this by:


Tapping and holding on an app icon on the home screen until the icons start to wiggle.
Tap the "x" icon on the Google Chrome app.
Open the App store.
Go the the farthest right tab - "Updates"
At the top will be "Purchased"
Scroll to Google Chrome and tap "Install".


After deleted the Chrome app, you can also just search the app store for "Google Chrome". When the Chrome app is displayed in the results, there will be an "Install" button. You can install it from there as well.