When you use Google Chrome to sign in to Outlook Web App in a Microsoft Exchange Server 2010 environment, the E-Mail Signature text box under the Settings tab is not editable.
This issue occurs because the rich text editor (RTE) for the E-mail Signature text box is disabled in Outlook Web App when you use Google Chrome.
To resolve this issue, install the update rollup that is described in the following article in the Microsoft Knowledge Base:
2685289 Description of Update Rollup 3 for Exchange Server 2010 Service Pack 2
Microsoft has confirmed that this is a problem in the Microsoft products that are listed in the "Applies to" section.