Chrome refers to the part of the Firefox window that lies outside of a window's content area. Toolbars, menu bars, progress bars, and window title bars are part of the Firefox browser chrome. It is in no way related to Google Chrome.
Chrome registration is something each Firefox add-on must do to work in Firefox. While some add-ons come with the appropriate chrome.manifest file, other add-ons rely on chrome.manifest being automatically generated when you start Firefox.
Chrome registration failure can occur when an add-on has come bundled with Firefox and you don't have system rights to edit files where Firefox is installed. (Thus chrome.manifest cannot be generated.)
To prevent this error from happening again, you need your system administrator to log on with an administrator account, and run Firefox at least once.
(Windows Vista & Windows 7) Right-click the Firefox icon in the desktop and select Run as Administrator.
If that isn't an option, you can disable the offending add-on.
At the top of the Firefox window, click the Tools menu, and select Add-ons.
The Add-ons window will open. In the Add-ons window, click the Extensions panel.
A list of installed extensions will be displayed. If you see any extension that you did not install yourself, select it, and click Disable.
Above the list of extensions, click Restart Firefox.
If the error still occurs, try disabling a different extension.
Extensions known to cause chrome registration failure
ThinkVantage Password Manager (bundled with Firefox in Lenovo Thinkpads)