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 \dot { P } = 1.120 ( 3 ) \times 10 ^ { -13 } \mbox { s s } ^ { -1 } . 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 3.4 \times 10 ^ { 13 } 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 roughly consistent with what was inferred earlier from the presence of a strong absorption feature in its X-ray spectrum . Furthermore , for both sources 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 .