Per Microsoft, you must have Windows 7 Professional, Enterprise, or Ultimate to run Windows XP Mode. However, even in Home Premium you can run apps in XP compatibility mode.
COLGeek is correct – in order to use Windows XP Mode and Windows Virtual PC you do need Windows 7 Professional, Windows 7 Enterprise or Windows 7 Ultimate. For those who do are not currently running Windows 7 Professional, Windows 7 Enterprise, or Windows 7 Ultimate, there is an easy upgrade path to Windows 7 Professional or Windows 7 Ultimate through the Windows Anytime Upgrade program.
Another alternative would be to test the application in compatibility mode first, prior to resorting to a virtual environment. A great web page to learn more about compatibility mode is Make older programs run in this version of Windows.