NTLM authentication should work just fine with Chrome, have you given a call into support to have us take a look at what you're seeing?
Also, are you using the default rules or some homemade rules? It would be a good idea to review this article if you have not: Web Gateway: Choosing the right Authentication Method for your Deployment
The rules seem to be named as though you are using the authentication server instead of direct proxy rules.
Often the rule traces might be confusing for first timers especially if you're not well versed in type1,type2, and type3 NTLM authentication messages.