The population of clearly identified anomalous X-ray pulsars has recently grown to seven, however, one candidate anomalous X-ray pulsar (AXP) still eludes re-confirmation. Here, we present a set of seven Chandra ACIS-S observations of the transient pulsar AX J1845.0-0258, obtained during 2003. Our observations reveal a faint X-ray point source within the ASCA error circle of AX J1845.0-0258s discovery, which we designate CXOU J184454.6-025653 and tentatively identify as the quiescent AXP. Its spectrum is well described by an absorbed single-component blackbody (kT~2.0 keV) or power law (Gamma~1.0) that is steady in flux on timescales of at least months, but fainter than AX J1845.0-0258 was during its 1993 period of X-ray enhancement by at least a factor of 13. Compared to the outburst spectrum of AX J1845.0-0258, CXOU J184454.6-025653 is considerably harder: if truly the counterpart, then its spectral behaviour is contrary to that seen in the established transient AXP XTE J1810-197, which softened from kT~0.67 keV to ~0.18 keV in quiescence. This unexpected result prompts us to examine the possibility that we have observed an unrelated source, and we discuss the implications for AXPs, and magnetars in general.