I've had the same thing happen. It's probably not limited to Chrome, but will show up in any browser because it seems to be a server problem.
Based on my experience, the problem occurs when you sign up for google apps and create users before your domain is verified. At least, this was my case.
The solution I found was to change the username after everything is verified. Once the username is changed, you should be able to log into the mail account without issue. You then have two options to continue to receive mail from the original address:
Add the original address as a nickname. This can be found in the settings area of your revised user.
Add a group, and make the group email address the name of your original email. Be sure to select the "Also allow anyone on the Internet to post messages" option when creating the group, or you will not receive any outside emails. Once the group is created, add the revised username as a member or owner.
I've seen a lot of people with this problem. Hope this helps!