  We present a phase-connected timing solution for the nearby isolated neutron
star RX J1308.6+2127 (RBS 1223). From dedicated Chandra observations as well as
archival Chandra and XMM-Newton data spanning a period of five years, we
demonstrate that the 10.31-sec pulsations are slowing down steadily at a rate
of Pdot=1.120(3)e-13 s/s. Under the assumption that this is due to magnetic
dipole torques, we infer a characteristic age of 1.5 Myr and a magnetic field
strength of 3.4e13 G. As with RX J0720.4-3125, the only other radio-quiet
thermally emitting isolated neutron star for which a timing solution has been
derived, the field strength is consistent with what was inferred earlier from
the presence of a strong absorption feature in its X-ray spectrum. Furthermore,
both sources share that the characteristic age is in excess of the cooling age
inferred from standard cooling models. The sources differ, however, in their
timing noise: while RX J0720.4-3125 showed considerable timing noise, RX
J1308.6+2127 appears relatively stable.
