Facebook Control is an excellent tool for parental control, and the only one in this field which lets you monitor the Facebook accounts being used on the web browser.
It maintains a log of all Facebook login attempts and sessions. In addition, it shows the total duration of all sessions.
Data is automatically synced across all computers where you are signed in to Chrome with your Google account. Thus, it is possible to monitor sessions on a computer from another device.
Also, it adds a Facebook button on the toolbar which links to facebook.com. Hide this button if you just want the control to be made in the background.
The log is accessed from the Options page of the extension. If you hide the button, you can find this option at
chrome://extensions/ or from Chrome menu > More tools > Extensions.