Chrome infinite loop trying to update - Galaxy Tab S
Typical solution for something like this:


Open Play Store
Swipe in from the left side and tap My apps
You'll see a list of apps installed, and at the top are apps that need updates, or are in the process of updating.
Find Chrome in the top section, tap on it, and tap the X on the right side of the status. This will stop the current download.
Head into your main system settings, Apps, and locate Chrome. It may be in the Downloaded section, or the All section, depending on whether it managed to download ANY updates at any point.
Tap on it, and then tap the UNINSTALL UPDATES button. If button doesn't exist, or is ghosted, continue to step 7.
Tap the CLEAR DATA and CLEAR CACHE buttons as well.
Restart your phone to play it safe.
Reopen Play Store and search for Chrome and attempt to manually force an update.
Come back here and comment about what happened.