We report on Very Large Array observations in the direction of the recently-discovered slow X-ray pulsar AX J1845-0258. In the resulting images, we find a 5-arcmin shell of radio emission; the shell is linearly polarized with a non-thermal spectral index. We class this source as a previously unidentified, young (< 8000 yr), supernova remnant (SNR), G29.6+0.1, which we propose is physically associated with AX J1845-0258. The young age of G29.6+0.1 is then consistent with the interpretation that anomalous X-ray pulsars (AXPs) are isolated, highly magnetized neutron stars (magnetars). Three of the six known AXPs can now be associated with SNRs; we conclude that AXPs are young (~<10 000 yr) objects, and that they are produced in at least 5% of core-collapse supernovae.