Two sensitive Chandra X-ray observations of the heavily-reddened galactic starburst cluster Westerlund 1 in May and June 2005 detected a previously unknown X-ray pulsar ( CXO J164710.20 - 455217 ) . Its slow 10.6 s pulsations , moderate X-ray temperature kT \approx 0.5 keV , and apparent lack of a massive companion tentatively suggest that it is an Anomalous X-ray Pulsar ( AXP ) . An isothermal blackbody model yields an acceptable spectral fit but the inferred source radius is much less than that of a neutron star , a result that has also been found for other AXPs . We analyze the X-ray spectra with more complex models including a model that assumes the pulsar is a strongly magnetized neutron star ( “ magnetar ” ) with a light element atmosphere . We conclude that the observed X-ray emission can not be explained as global surface emission arising from the surface of a cooling neutron star or magnetar . The emission likely arises in one or more localized regions ( “ hot spots ” ) covering a small fraction of the surface . We discuss these new results in the context of both accretion and magnetar interpretations for the X-ray emission .