Middle-aged, cooling neutron stars are observed both as relatively rapidly spinning radio pulsars and as more slowly spinning, strongly magnetized isolated neutron stars (INSs), which stand out by their thermal X-ray spectra. The difference between the two classes may be that the INSs initially had much stronger magnetic fields, which decayed. To test this, we used the Chandra X-ray Observatory to observe 1RXS J072559.8−261229, a possible X-ray counterpart to PSR J0726−2612, which, with its 3.44 s period and 3×10 13 G inferred magnetic field strength, is the nearest and least extincted among the possible slowly spinning, strong-field INS progenitors (it likely is in the Gould Belt, at ∼1 kpc). We confirm the identification and find that the pulsar has a spectrum consistent with being purely thermal, with blackbody temperature kT = 87 ± 5 eV and radius R = 5.7 +2.6 −1.3 km at a distance of 1 kpc. We detect sinusoidal pulsations at twice the radio period with a semi-amplitude of 27% ± 5%. The properties of PSR J0726−2612 strongly resemble those of the INSs, except for its much shorter characteristic age of 200 kyr (instead of several Myr). We conclude that PSR J0726−2612 is indeed an example of a young INS, one that started with a magnetic field strength on the low end of those inferred for the INSs, and that, therefore, decayed by a relatively small amount. Our results suggest that the long-period, strong-field pulsars and the INSs are members of the same class, and open up new opportunities to understand the puzzling X-ray and optical emission of the INSs through radio observations of PSR J0726−2612.