I came across this solution when I was looking to recover tabs that had been permanently closed after my browser crashed one day. In order to access the information you require, you device needs to be rooted and should have a file explorer app that can access the root files installed on your device. [ES File Explorer][1] or [Root Explorer][2] are my recommendations.  

1. Navigate to the root folder of your device (the protected system partition) → select `DATA` → select `com.android.chrome`.  

2. There are several places where you may find information about your current tabs. 
 
 1. The first folder to check is `app_tabs`, then `0`. In this folder there should be a file called `tab_state` which contains a list of all your current tabs. 
 2. There are also other files in this folder called `tab3`, `tab4`, etc. that contain info about current tabs.
 3. IMO, you need a special "text editor / sql editor" to read the content of some of these files as the encoding is different. 


3. Next place to look is `/data/com.android.chrome/app_chrome/Default/`. In this folder you'll find a file called `History`. Depending on your situation, you may find a good list of recent site visits here. 

4. Finally, navigate to the `Sync Data folder`. In here, you will find the information that's being synced to Google (and this should include all the tabs you currently have synced on other devices). 
 - In the file `SyncData.sqlite3`, you'll also find a history of all your Google searches (which I sometimes find to be an interesting read). 
 - You'll need an Sqlite3 data browser [program][3] on your PC in order to read this file.  The app should be able to export to a highly usable `.CSV` or `.XLS` file that you can open in **MS Excel**. 

This could be helpful to someone I assume.   


[1]: https://play.google.com/store/apps/details?id=com.estrongs.android.pop
[2]: https://play.google.com/store/apps/details?id=com.speedsoftware.rootexplorer
[3]: http://sqlitebrowser.org/