I don't believe this kind of information is going to be exposed. You might be better off looking for this data at the network level via something like deep packet inspection.

There is no such function for Chrome, but Soti Surf secure browser does supports log/history file which can be synced back to MobiControl server via file-sync rule.

I agree with Matt.  You are better off with a proxy server that will help monitor traffic and just block the traffic you do not want.  Plus you should have insight into the most visited sites and those that spend too much time just surfing.