David,
My argument would be that since IE and Firefox behave normally when authenticating to the internal ADFS then that would rule out a network/dns issue. Since Chrome authenticates consistently to the external ADFS server that indicates that Chrome functions correctly with Office 365.
The most likely cause, from my perspective, is the internal ADFS itself. The problems we have seen are always authentication based which doesn't involve O365. This is supported by the other postings I have found which seem to have no variation in symptoms.
One workaround that appears to be working is to have the Chrome users enter only their username and password versus using their UPN and password. This is confusing to the users since they have to enter their UPN at the actual Office 365 website, and then enter just the username in the authentication box. I am hoping that Microsoft will take this matter seriously and not assume that it is a Chrome issue.
Brian Harrell
Senior Systems Engineer