Trying to open a sharepoint library in Windows Explorer via IE 8 results in the error "your client does not support opening this list with windows explorer"

I am attempting to connect to a Microsoft Sharepoint library, via the "Actions -> Open in Windows Explorer" option from the Sharepoint page.  When I do so, I get the error message "your client does not support opening this list with windows explorer".  In short, I am trying to get the "drag and drop" functionality of a Sharepoint library.

I am running Windows 7 64-bit and IE8.  The target Sharepoint environment is a MOSS 2007 EE.  My Windows "WebClient" service is running, and I have no problem connecting to this exact library via a Windows XP computer running IE8.