Using X-ray data from the Rossi X-ray Timing Explorer, we report the pulse
timing results of the accretion-powered, high-mass X-ray binary pulsar 4U 1
907 + 09, covering a time-span of almost two years. We measured three new p
ulse periods in addition to the previously measured four pulse periods. We
are able to connect pulse arrival times in phase for more than a year. The
source has been spinning down almost at a constant rate, with a spin-down r
ate of (nu) over dot = (- 3.54 +/- 0.02) x 10(-14) Hz s(-1) for more than 1
5 yr. Residuals of pulse arrival times yield a very low level of random-wal
k noise, with a strength of similar to2 x 10(-20) rad(2) s(-3) on a time-sc
ale of 383 d, which is 40 times lower than that of the high-mass X-ray bina
ry pulsar Vela X-1. The noise strength is only a factor of 5 greater than t
hat of the low-mass X-ray binary pulsar 4U 1626-67. The low level of the ti
ming noise and the very stable spin-down rate of 4U 1907+09 make this sourc
e unique among the high-mass X-ray binary pulsars, providing another exampl
e, in addition to 4U 1626-67, of long-term quiet spin down from an accretin
g source. These examples show that the extended quiet spin-down episodes ob
served in the anomalous X-ray pulsars 1RXS J170849.0-400910 and IE 2259+586
do not necessarily imply that these sources are not accreting pulsars.