Covenant Eyes will monitor Chrome if it's the stock system browser, whether it's in incognito mode or not. If Chrome isn't the stock system browser, it will tell you how long has been spent in the app, but can't actually monitor the browser activity. From their description:
"
monitors and reports websites visited through the stock browser, Dolphin Browser, and Skyfire Web Browser. In addition, it reports when and for how long other apps were accessed."
So basically if Chrome happens to be the stock browser, it'll monitor it, regardless of incognito mode. I believe only the newer Moto devices and Nexus devices have Chrome as the actual system browser, though.
Also, it's not free - but it works! It also shows apps installed and time spent in each app.
Hopefully that made sense... typed that out in a bit of a hurry!