Make sure your version of Chrome is up to date. I'm using Chrome also and can see the inventory just fine.
If your version is up to date, then it is possible a plugin or addon could be interfering with your ability to see the inventory.
To check for this, click the wrench icon, choose "New Incognito Window" and proceed to login to Res using that. If you are able to see it at that point, then you know you have some sort of extra installed to the browser that is causing the issue.
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