Galaxy S3 randomly booted into safe mode. Strange behavior
This is strange, and is most certainly a software issue.

It could be that, for some reason or another, Chrome (or another background app) took up all the available RAM, which caused the OS to crash - it could be a built in safeguard that the device boots into safe mode when this happens.

As well as this, safe mode (on my old device at least), disables all 3rd-party apps (so you can debug, and see if an app is causing the issue).

I would suggest you check your RAM usage, and maybe do a clean wipe if it happens again.