Chrome allows you to set up a separate profile for your kids, which you monitor and control. First, create a new profile by going to 'Settings->People->Manage Other People->Add Person'. Click on the checkbox next to 'Control and view the websites this person visits from; and click 'Add'. A few minutes later, you'll receive an email link leading you to the supervised user's page.
Once there, you'll have the ability to block certain sites, keep SafeSearch on lock, and view that user's web activities. You can then log your kids into Chrome under their own identity by clicking 'Settings->Manage Other People' and clicking on their profile.