We analyze all X-ray timing data on 1E 1207.4-5209 in supernova remnant PKS 1209-51/52 gathered in 2000-2005, and find a highly stable rotation with P=424.130451(4) ms and period derivative of (9.6 +/- 9.4)E-17 s/s. This refutes previous claims of large timing irregularities in these data. In the dipole spin-down formalism, the 2-sigma upper limit on period derivative implies an energy loss rate < 1.5E32 ergs/s, surface magnetic field strength B_p < 3.5E11 G, and characteristic age tau > 24 Myr. This tau exceeds the remnant age by 3 orders of magnitude, requiring that the pulsar was born spinning at its present period. The X-ray luminosity of 1E 1207.4-5209, L(bol) ~= 2E33 ergs/s at 2 kpc, exceeds its spin-down energy loss, implying that L(bol) derives from residual cooling, and perhaps partly from accretion of supernova debris. The upper limit on B_p is small enough to favor the electron cyclotron model for at least one of the prominent absorption lines in its soft X-ray spectrum. This is the second demonstrable case of a pulsar born spinning slowly and with a weak B-field, after PSR J1852+0040 in Kesteven 79. Comment: 5 pages, 2 figure, Latex, emulateapj style. Submitted to ApJ Letters