To see if this is happening, close Chrome, and then start Windows Task Manager (e.g., by right-clicking on the Taskbar) and check for "chrome.exe" in the Processes tab.
To keep this from happening:
- Start Chrome.
- Click icon Customize and Control Google Chrome at top right corner, and then click Settings from the drop-down menu.
- Scroll to the bottom of the Settings window, and then click Show advanced settings...
- Scroll again to the bottom of the Settings window, and then uncheck Continue running background apps when Google Chrome is closed.