Your server cert might already be properly chained with intermediate cert(s) to a root cert in the browser (ie the browser already has the intermediate cert(s) and root cert installed). You can check this by viewing the cert in IE and then clicking on the Certification Path.
I don't think you need to install the root cert in the chain as the client has to have it in order to avoid the unchained (or untrusted) cert error. It doesn't hurt to include the intermediate cert(s) in the bundle for non-standard clients who might not already have it/them installed.
Aaron
Cirrostratus